南京大学学报（数学半年刊）
南京大學學報（數學半年刊）
남경대학학보（수학반년간）
JOURNAL OF NANJING UNIVERSITY MATHEMATICAL BIQUARTERLY
2005年
2期
299-307
,共9页
序S-系%grothendieck群%强凸S-子系
序S-繫%grothendieck群%彊凸S-子繫
서S-계%grothendieck군%강철S-자계
S-posets%Grothendieck groups%strongly convex S-subposets
设S为幺半群,1为其单位元,B是非空集合.若有映射(S在B上的作用)S×B→B满足s(tb)=(st)b,1b=b,其中s,t∈S,b∈B,则称B为(左)S-系.宋光天利用有限生成投射S-系讨论了半群的Grothendieck群和Whitehead群.在文[6]中,作者给出了无零元序幺半群S上的投射序S-系的结构.本文首先利用不可分强凸子系给出了序S-系的分解定理,然后给出了投射序S-系的结构,最后讨论了序半群上的Grothendieck群.
設S為幺半群,1為其單位元,B是非空集閤.若有映射(S在B上的作用)S×B→B滿足s(tb)=(st)b,1b=b,其中s,t∈S,b∈B,則稱B為(左)S-繫.宋光天利用有限生成投射S-繫討論瞭半群的Grothendieck群和Whitehead群.在文[6]中,作者給齣瞭無零元序幺半群S上的投射序S-繫的結構.本文首先利用不可分彊凸子繫給齣瞭序S-繫的分解定理,然後給齣瞭投射序S-繫的結構,最後討論瞭序半群上的Grothendieck群.
설S위요반군,1위기단위원,B시비공집합.약유영사(S재B상적작용)S×B→B만족s(tb)=(st)b,1b=b,기중s,t∈S,b∈B,칙칭B위(좌)S-계.송광천이용유한생성투사S-계토론료반군적Grothendieck군화Whitehead군.재문[6]중,작자급출료무령원서요반군S상적투사서S-계적결구.본문수선이용불가분강철자계급출료서S-계적분해정리,연후급출료투사서S-계적결구,최후토론료서반군상적Grothendieck군.
For a monoid S, a (left) S-act is a non-empty set B together with a mappingS × B → B sending (s, b) to sb such that s(tb) = (st)b and 1b = b for all s, t ∈ S andb ∈ B. Using the category of finitely generated projective S-acts, Song introducedthe Grothendieck groups and the Whitehead groups of semigroups. Partially orderedacts over a partially ordered monoid S, or S-posets, appear naturally in the studyof mappings between posets. Recently, projective S-posets without zero element areconsidered. In this paper, a unique decomposition theorem of S-posets is given in termsof strongly convex, indecomposable S-subposets, and a structure theorem for projectiveS-posets is given. In the last section, we discuss the Grothendieck groups of partiallyordered semigroups.
