一类广义正则半环上可除半环同余的等价刻画

研究了一类广义正则半环的理想,利用这类理想,得到了这类半环上同余的几种刻画.     

一类广义正则半环上同余的特征

在半环中引入了一类理想的概念,讨论了这类理想的性质,并研究了一类广义正则半环上的同余,给出了这类半环上一种半环同余的特征．     

关于拟正则半环上可除半环同余的注记

研究了拟正则半环上的同余,给出了拟正则半环上一类理想的性质,并利用这类理想给出了拟正则半环上可除半环同余的几种等价形式.     

半环的理想与同余

引入半环的完全素理想的概念.利用这一概念,研究了半环的同余,分别给出了半环的子直积分解的若干结果和同余的一种刻画.     

某些完全正则半环的刻画

研究了完全正则半环的特征.利用半群的方法,得到了当分配半环的乘法幂等元集分别是左零带、矩形带以及正规带时,该类半环成为完全正则半环的等价刻画,推广并改进了相关文献的主要结果.     

半环上的素同余和同余的根

主要研究了可换幂等元半环的同余.给出了素同余和同余的根的一些结果,且揭示了同余ρ的根与包含ρ的素同余的全体之间的关系.     

半环的强分配格上的环同余

主要讨论了在一定条件下半环的强分配格S上的环同余ρ与半环族{Sα}α∈D上的环同余族{ρα}α∈D之间的关系.     

可补半环上的同余

研究可补丰环上的同余关系,得出一些重要性质.并证明了一个半环R是可补半环当且仅当它是某个布尔环和布尔代数的直积,因而可补半环必是来法可交换的.     

关于半环上格林关系的开同余

首先给出了由半环的乘法半群上的格林关系所确定的半环开同余的性质和刻画.其次,由开同余出发,得到了六个不同的半环类,并证明了这六个半环类均是半环簇.最后,对半环簇的子簇格上的开算子进行了探讨,得到了一些有趣的结果.     

加法幂等元满足置换等式的纯整半环上的同余

广义逆半群上的同余早已开始研究.在这类半群的性质研究基础上,本文主要给出了加法幂等元满足置换等式的纯整半环上的同余刻画,并且给出了这类半环的同态像的一个结构定理.     

分配半环上的可除半环同余

§ 1.　Introduction　　AsemiringSisanalgebraicsystem (S ,+ ,·)consistingofanon_emptysetStogetherwithtwobinaryoperations +and·onSsuchthat (S ,+ )and (S ,·)aresemigrolupscon nectedbyring_likedistributivity .AsemiringSiscalleddistributiveifinStheadditionisdis tributiveaboutmultiplication ,i.e .ab+c=(a+c) (b +c)anda+bc=(a +b) (a+c)holdforalla ,b ,c∈S .AsemiringSiscalleddivisibleif(S ,·)isagroup .AnequivalencerelationρonasemiringSiscalledacongruenceonS ,iffρisacongruenceon (S ,+ )and (…     

序半环的序理想

An ordered semiring is a semiring S equipped with a partial order ≤ such that the operations are monotonic and constant 0 is the least element of S.In this paper,several notions,for example,ordered ideal,minimal ideal,and maximal ideal of an ordered semiring,simple ordered semirings,etc.,are introduced.Some properties of them are given and characterizations for minimal ideals are established.Also,the matrix semiring over an ordered semiring is consid-ered.Partial results obtained in this paper are analogous to the corresponding ones on ordered semigroups,and on the matrix semiring over a semiring.     

Semirings which are unions of rings

Sernirings which are a disjoint union of rings form a variety S which contains the variety of all rings and the variety of all idempotent sernirings, and in particular, the variety of distributive lattices. Various structure theorems are established which bring insight into the structure of the lattice of subvarieties of S.``     

Congruences and ideals in ternary rings

A ternary ring is an algebraic structure R=(R,t0.1) of type (3, 0, 0) satisfying the identities t(0, x, y) = y = t(x, 0, y) and t(1, x, 0) = x = (x, l, 0) where, moreover, for any a, b, c R there exists a unique d R with t(a, b, d) = c. A congruence on R is called normal if R with t is a ternary ring again. We describe basic properties of the lattice of all normal congruences on R and establish connections between ideals (introduced earlier by the third author) and congruence kernels.