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function_rings [2010/07/29 15:46] external edit
function_rings [2012/06/16 04:47] (current)
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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====
Only the one-element $f$-ring. Only the one-element $f$-ring.
====Subclasses==== ====Subclasses====