摘要
平坦半环是一类重要的加法幂等元半环,它在半环簇理论的研究中扮演着重要的角色.主要研究了次直不可约的平坦半环,以及一类平坦半环生成的簇.给出了次直不可约的nil-平坦半环的等价刻画,证明了当n小于4时,平坦半环S(x_(1)x_(2)···x_(n))均是有限基底的.
Flat semirings is an important class of additively idempotent semirings.It has played an important role in the study of semiring varieties.In this paper subdirectly irreducible flat semirings and the varieties generated by some flat semirings are studied.Some characterizations of subdirectly irreducible flat nilsemirings are given.It is shown that the variety generated by each flat semiring S(x_(1)x_(2)…x_(n))is finitely based for linear words x_(1)x_(2)…x_(n) in X^(+),n less than 4.
作者
高子东
任苗苗
Gao Zidong;Ren Miaomiao(School of Mathematics,Northwest University,Xi′an 710127,China)
出处
《纯粹数学与应用数学》
2022年第1期79-90,共12页
Pure and Applied Mathematics
基金
国家自科学基金(11701449,11971383,11571278,11801239)
陕西省自然科学基金(2022JM-009).
关键词
ai-半环
平坦半环
半环同余
半环簇
ai-semiring
flat semiring
semiring congruence
semiring variety
