# Differences

This shows you the differences between two versions of the page.

function_rings [2010/07/29 15:46] 127.0.0.1 external edit |
function_rings [2012/06/16 04:47] (current) jipsen |
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Abbreviation: **FRng** | Abbreviation: **FRng** | ||

====Definition==== | ====Definition==== | ||

- | A \emph{function ring} (or $f$\emph{-ring}) is an | + | A \emph{function ring} (or $f$\emph{-ring}) is a |

- | [[Lattice-ordered rings]] $\mathbf{F}=\langle F,\vee,\wedge,+,-,0,\cdot\rangle$ such that | + | [[lattice-ordered rings|lattice-ordered ring]] $\mathbf{F}=\langle F,\vee,\wedge,+,-,0,\cdot\rangle$ such that |

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^[[Congruence regular]] |yes, see [[groups]] | | ^[[Congruence regular]] |yes, see [[groups]] | | ||

^[[Congruence uniform]] |yes, see [[groups]] | | ^[[Congruence uniform]] |yes, see [[groups]] | | ||

- | |||

^[[Definable principal congruences]] | | | ^[[Definable principal congruences]] | | | ||

^[[Equationally def. pr. cong.]] | | | ^[[Equationally def. pr. cong.]] | | | ||

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====Finite members==== | ====Finite members==== | ||

- | $\begin{array}{lr} | ||

Only the one-element $f$-ring. | Only the one-element $f$-ring. | ||

- | \end{array}$ | ||

====Subclasses==== | ====Subclasses==== |

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