# Differences

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index.html [2016/08/05 05:27] jipsen |
index.html [2019/12/10 17:29] (current) pnotthesamejipsen |
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what properties are known about these structures. | what properties are known about these structures. | ||

- | These pages are currently still under construction. Knowledgeable readers are encouraged to add or correct information. | + | These pages are currently still under construction. /*Knowledgeable readers are encouraged to email additions or corrections to Peter Jipsen add or correct information.*/ |

- | To enable the edit button on each page, use the Login link (above) to log in or create an account. | + | /*To enable the edit button on each page, use the Login link (above) to log in or create an account.*/ |

Initially the main content concerns mostly first-order classes of relational | Initially the main content concerns mostly first-order classes of relational | ||

structures and, more particularly, equationally defined classes of algebraic structures. | structures and, more particularly, equationally defined classes of algebraic structures. | ||

- | If you are familiar with some of these classes of structures, feel | + | If you are familiar with some of these classes of structures and would like some information added, please email Peter Jipsen (jipsen@chapman.edu). [Account creation unfortunately had to be disabled.] /*feel |

free to add some relevant information and references by using the edit | free to add some relevant information and references by using the edit | ||

link on the respective page. Pages are written in DokuWiki syntax, but mathematical notation is in standard LaTeX. | link on the respective page. Pages are written in DokuWiki syntax, but mathematical notation is in standard LaTeX. | ||

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versions of these pages are still available at http://math.chapman.edu/cgi-bin/structures.pl and http://math.chapman.edu/cgi-bin/structures . | versions of these pages are still available at http://math.chapman.edu/cgi-bin/structures.pl and http://math.chapman.edu/cgi-bin/structures . | ||

You can use this [[Sandbox]] page to try out editing (without worrying about deleting | You can use this [[Sandbox]] page to try out editing (without worrying about deleting | ||

- | useful information). | + | useful information).*/ |

- | [[Suggestions or comments]]? Just follow the link and edit the page. | + | /*[[Suggestions or comments]]? Just follow the link and edit the page.*/ |

**New:** Boldface links below display lists of finite algebras in a particular class (calculated locally in the browser). | **New:** Boldface links below display lists of finite algebras in a particular class (calculated locally in the browser). | ||

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-[[Bilattices]] | -[[Bilattices]] | ||

-[[Bilinear algebras]] | -[[Bilinear algebras]] | ||

- | -[[Basic logic algebras|BL-algebras]] | ||

-[[Binars]], **[[Finite binars]], [[Finite binars with identity|with identity]], [[Finite binars with zero|with zero]], [[Finite binars with identity and zero|with identity and zero]]**, | -[[Binars]], **[[Finite binars]], [[Finite binars with identity|with identity]], [[Finite binars with zero|with zero]], [[Finite binars with identity and zero|with identity and zero]]**, | ||

+ | -[[Basic logic algebras|BL-algebras]] | ||

-[[Boolean algebras]] nbsp [[wp>Boolean algebra (structure)]] | -[[Boolean algebras]] nbsp [[wp>Boolean algebra (structure)]] | ||

-[[Boolean algebras with operators]] | -[[Boolean algebras with operators]] | ||

Line 77: | Line 77: | ||

-[[Cancellative commutative semigroups]] | -[[Cancellative commutative semigroups]] | ||

-[[Cancellative monoids]] | -[[Cancellative monoids]] | ||

+ | -[[Cancellative partial monoids]] | ||

-[[Cancellative semigroups]] | -[[Cancellative semigroups]] | ||

-[[Cancellative residuated lattices]] | -[[Cancellative residuated lattices]] | ||

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-[[Commutative BCK-algebras]] | -[[Commutative BCK-algebras]] | ||

-[[Commutative binars]], **[[Finite commutative binars]], [[Finite commutative binars with identity|with identity]], [[Finite commutative binars with zero|with zero]], [[Finite commutative binars with identity and zero|with identity and zero]]** | -[[Commutative binars]], **[[Finite commutative binars]], [[Finite commutative binars with identity|with identity]], [[Finite commutative binars with zero|with zero]], [[Finite commutative binars with identity and zero|with identity and zero]]** | ||

+ | -[[Commutative idempotent involutive residuated lattices]] | ||

-[[Commutative integral ordered monoids]], **[[Finite commutative integral ordered monoids]]** | -[[Commutative integral ordered monoids]], **[[Finite commutative integral ordered monoids]]** | ||

-[[Commutative inverse semigroups]] | -[[Commutative inverse semigroups]] | ||

+ | -[[Commutative involutive FL-algebras]] | ||

+ | -[[Commutative involutive residuated posets]] | ||

-[[Commutative lattice-ordered monoids]] | -[[Commutative lattice-ordered monoids]] | ||

-[[Commutative lattice-ordered rings]] | -[[Commutative lattice-ordered rings]] | ||

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-[[Directed complete partial orders|Complete partial orders]] | -[[Directed complete partial orders|Complete partial orders]] | ||

-[[Completely regular Hausdorff spaces]] | -[[Completely regular Hausdorff spaces]] | ||

- | -[[Completely regular semigroups]] | + | -[[wp>Completely regular semigroups]] |

+ | -[[Conjugative binars]] | ||

-[[Continuous lattices]] | -[[Continuous lattices]] | ||

-[[Continuous posets]] | -[[Continuous posets]] | ||

+ | -[[Cyclic involutive FL-algebras]] | ||

+ | -[[Cyclic involutive residuated posets]] | ||

-[[Cylindric algebras]] | -[[Cylindric algebras]] | ||

-[[De Morgan algebras]] | -[[De Morgan algebras]] | ||

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-[[Distributive double p-algebras]] | -[[Distributive double p-algebras]] | ||

-[[Distributive dual p-algebras]] | -[[Distributive dual p-algebras]] | ||

+ | -[[Distributive involutive residuated lattices]] | ||

-[[Distributive lattice expansions]] | -[[Distributive lattice expansions]] | ||

-[[Distributive lattices]] | -[[Distributive lattices]] | ||

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-[[Dunn monoids]] | -[[Dunn monoids]] | ||

-[[Dynamic algebras]] | -[[Dynamic algebras]] | ||

+ | -[[Effect algebras]] | ||

-[[Medial groupoids|Entropic groupoids]] | -[[Medial groupoids|Entropic groupoids]] | ||

-[[Equivalence algebras]] | -[[Equivalence algebras]] | ||

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-[[FL-algebras]] | -[[FL-algebras]] | ||

-[[FLc-algebras]] | -[[FLc-algebras]] | ||

+ | -[[Heyting algebras|FLcw-algebras]] | ||

-[[FLe-algebras]] | -[[FLe-algebras]] | ||

+ | -[[FLec-algebras]] | ||

+ | -[[Heyting Algebras|FLecw-algebras]] | ||

-[[FLew-algebras]] | -[[FLew-algebras]] | ||

+ | -[[FLi-algebras]] | ||

+ | -[[FLo-algebras]] | ||

-[[FLw-algebras]] | -[[FLw-algebras]] | ||

-[[Frames]] | -[[Frames]] | ||

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-[[Generalized BL-algebras]] | -[[Generalized BL-algebras]] | ||

-[[Generalized Boolean algebras]] | -[[Generalized Boolean algebras]] | ||

+ | -[[Generalized effect algebras]] | ||

-[[Generalized MV-algebras]] | -[[Generalized MV-algebras]] | ||

- | -[[Goedel algebras]] | + | -[[Generalized orthoalgebras]] |

+ | -[[Generalized pseudo-effect algebras]] | ||

+ | -[[Generalized separation algebras]] | ||

+ | -[[Gödel algebras]] | ||

-[[Graphs]] | -[[Graphs]] | ||

-[[Groupoids]] | -[[Groupoids]] | ||

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-[[Hilbert spaces]] | -[[Hilbert spaces]] | ||

-[[Hoops]] | -[[Hoops]] | ||

+ | -[[Idempotent residuated lattices]] | ||

+ | -[[Idempotent involutive residuated lattices]] | ||

-[[Idempotent semirings]] | -[[Idempotent semirings]] | ||

-[[Idempotent semirings with identity]] | -[[Idempotent semirings with identity]] | ||

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-[[Implicative lattices]] | -[[Implicative lattices]] | ||

-[[Integral domains]] | -[[Integral domains]] | ||

+ | -[[Integral involutive FL-algebras]] | ||

-[[Integral ordered monoids]], **[[finite integral ordered monoids]]** | -[[Integral ordered monoids]], **[[finite integral ordered monoids]]** | ||

-[[Integral relation algebras]] | -[[Integral relation algebras]] | ||

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-[[Involutive lattices]] | -[[Involutive lattices]] | ||

-[[Involutive FL-algebras|Involutive residuated lattices]] | -[[Involutive FL-algebras|Involutive residuated lattices]] | ||

+ | -[[Involutive residuated posets]] | ||

-[[Join-semidistributive lattices]] | -[[Join-semidistributive lattices]] | ||

-[[Semilattices|Join-semilattices]] | -[[Semilattices|Join-semilattices]] | ||

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-[[Kleene logic algebras]] | -[[Kleene logic algebras]] | ||

-[[Residuated partially ordered semigroups|Lambek algebras]] | -[[Residuated partially ordered semigroups|Lambek algebras]] | ||

+ | -[[Lattice effect algebras]] | ||

+ | -[[Lattice implication algebras]] | ||

-[[Lattice-ordered groups]] | -[[Lattice-ordered groups]] | ||

-[[Lattice-ordered monoids]] | -[[Lattice-ordered monoids]] | ||

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-[[Lattices]] | -[[Lattices]] | ||

-[[Left cancellative semigroups]] | -[[Left cancellative semigroups]] | ||

+ | -[[Left neofield]] | ||

-[[Lie algebras]] | -[[Lie algebras]] | ||

+ | -[[Commutative residuated partially ordered monoids|Lineales]] | ||

-[[Goedel algebras|Linear Heyting algebras]] | -[[Goedel algebras|Linear Heyting algebras]] | ||

-[[Linear logic algebras]] | -[[Linear logic algebras]] | ||

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-[[Lukasiewicz algebras of order n]] | -[[Lukasiewicz algebras of order n]] | ||

-[[M-sets]] | -[[M-sets]] | ||

+ | -[[Binars|Magmas]] | ||

-[[Medial groupoids]] | -[[Medial groupoids]] | ||

-[[Medial quasigroups]] | -[[Medial quasigroups]] | ||

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-[[Multisets]] | -[[Multisets]] | ||

-[[MV-algebras]] | -[[MV-algebras]] | ||

+ | -[[MV-effect algebras]] | ||

+ | -[[m-zeroids]] | ||

-[[Neardistributive lattices]] | -[[Neardistributive lattices]] | ||

-[[Near-rings]] | -[[Near-rings]] | ||

-[[Near-rings with identity]] | -[[Near-rings with identity]] | ||

-[[Near-fields]] | -[[Near-fields]] | ||

+ | -[[Neofields]] | ||

-[[Nilpotent groups]] | -[[Nilpotent groups]] | ||

-[[Nonassociative relation algebras]] | -[[Nonassociative relation algebras]] | ||

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-[[Partially ordered sets|Ordered sets]] | -[[Partially ordered sets|Ordered sets]] | ||

-[[Ore domains]] | -[[Ore domains]] | ||

+ | -[[Orthoalgebras]] | ||

-[[Ortholattices]] | -[[Ortholattices]] | ||

-[[Orthomodular lattices]] | -[[Orthomodular lattices]] | ||

-[[p-groups]] | -[[p-groups]] | ||

-[[Partial groupoids]] | -[[Partial groupoids]] | ||

+ | -[[Partial monoid]] | ||

-[[Partial semigroups]] | -[[Partial semigroups]] | ||

-[[Partially ordered groups]] | -[[Partially ordered groups]] | ||

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-[[FL-algebras|Pointed residuated lattices]] | -[[FL-algebras|Pointed residuated lattices]] | ||

-[[Polrims]] | -[[Polrims]] | ||

- | -[[Polyadic algebras]] | + | -[[wp>Polyadic algebras]] |

-[[Partially ordered sets|Posets]] | -[[Partially ordered sets|Posets]] | ||

-[[Post algebras]] | -[[Post algebras]] | ||

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-[[Process algebras]] | -[[Process algebras]] | ||

-[[Pseudo basic logic algebras]] | -[[Pseudo basic logic algebras]] | ||

+ | -[[Pseudo-effect algebras]] | ||

-[[Pseudo MTL-algebras]] | -[[Pseudo MTL-algebras]] | ||

-[[Pseudo MV-algebras]] | -[[Pseudo MV-algebras]] | ||

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-[[Residuated partially ordered monoids]] | -[[Residuated partially ordered monoids]] | ||

-[[Residuated partially ordered semigroups]] | -[[Residuated partially ordered semigroups]] | ||

+ | -[[Residuated partially ordered monoids|Residuated posets]] | ||

+ | -[[Right residuated binars]] | ||

+ | -[[Right hoops]] | ||

+ | -[[Right quasigroups]] | ||

-[[Rings]] | -[[Rings]] | ||

-[[Rings with identity]] | -[[Rings with identity]] | ||

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-[[Semiassociative relation algebras]] | -[[Semiassociative relation algebras]] | ||

-[[Semidistributive lattices]] | -[[Semidistributive lattices]] | ||

+ | -[[Semifields]] | ||

-[[Semigroups]], **[[Finite semigroups]]** | -[[Semigroups]], **[[Finite semigroups]]** | ||

-[[Monoids|Semigroups with identity]] | -[[Monoids|Semigroups with identity]] | ||

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-[[Semirings with identity and zero]] | -[[Semirings with identity and zero]] | ||

-[[Semirings with zero]] | -[[Semirings with zero]] | ||

+ | -[[Separation algebras]] | ||

-[[Sequential algebras]] | -[[Sequential algebras]] | ||

-[[Sets]] | -[[Sets]] | ||

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-[[Steiner quasigroups]] | -[[Steiner quasigroups]] | ||

-[[Stone algebras]] | -[[Stone algebras]] | ||

+ | -[[Sugihara algebras]] | ||

+ | -[[Sugihara monoids]] | ||

-[[Symmetric relations]] | -[[Symmetric relations]] | ||

-[[T0-spaces]] | -[[T0-spaces]] |

Trace: