翻訳と辞書 Words near each other ・ Maximal (Transformers) ・ Maximal arc ・ Maximal common divisor ・ Maximal compact subgroup ・ Maximal Crazy ・ Maximal element ・ Maximal ergodic theorem ・ Maximal evenness ・ Maximal function ・ Maximal ideal ・ Maximal independent set ・ Maximal information coefficient ・ Maximal lotteries ・ Maximal munch ・ Maximal pair ・ Maximal semilattice quotient ・ Maximal set ・ Maximal subgroup ・ Maximal torus ・ Maximal-ratio combining ・ Maximalism ・ Maximalist! (band) ・ Maximally informative dimensions ・ Maximally stable extremal regions ・ Maximaphily ・ Maximato ・ Maxime ・ Maxime (film) ・ Maxime Agueh ・ Maxime Alexandre Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Maximal semilattice quotient ： ウィキペディア英語版 Maximal semilattice quotient In abstract algebra, a branch of mathematics, a maximal semilattice quotient is a commutative monoid derived from another commutative monoid by making certain elements equivalent to each other. Every commutative monoid can be endowed with its ''algebraic'' preordering ≤ . By definition, ''x≤ y'' holds, if there exists ''z'' such that ''x+z=y''. Further, for ''x, y'' in ''M'', let $x\backslash propto\; y$ hold, if there exists a positive integer ''n'' such that ''x≤ ny'', and let $x\backslash asymp\; y$ hold, if $x\backslash propto\; y$ and $y\backslash propto\; x$. The binary relation $\backslash asymp$ is a monoid congruence of ''M'', and the quotient monoid $M/$ is the ''maximal semilattice quotient'' of ''M''. This terminology can be explained by the fact that the canonical projection ''p'' from ''M'' onto $M/$ is universal among all monoid homomorphisms from ''M'' to a (∨,0)-semilattice, that is, for any (∨,0)-semilattice ''S'' and any monoid homomorphism ''f: M→ S'', there exists a unique (∨,0)-homomorphism $g\backslash colon\; M/\backslash to\; S$ such that ''f=gp''. If ''M'' is a refinement monoid, then $M/$ is a distributive semilattice. ==References== A.H. Clifford and G.B. Preston, The Algebraic Theory of Semigroups. Vol. I. Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I. 1961. xv+224 p. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Maximal semilattice quotient」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.