关于加法幂等元半环簇的几个结果  

Some results on varieties of additively idempotent semirings

作　　者：任苗苗 赵宪钟 Ren Miaomiao;Zhao Xianzhong(School of Mathematics, Northwest University, Xi′an 710027, China)

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《纯粹数学与应用数学》2018年第4期406-410,共5页Pure and Applied Mathematics

基　　金：国家自然科学基金(11701449;11571278);陕西省自然科学基础研究计划项目(2017JQ1033);陕西省教育厅专项科研计划项目(16JK1754);西北大学科学研究基金(15NW24)

摘　　要：证明了若一个加法幂等元半环是遗传非有限基底的,则它的乘法导出也是遗传非有限基底的.作为该结果的应用,表明了满足恒等式x^n≈x的有限加法幂等元半环和阶数小于6的加法幂等元半环都不是遗传非有限基底的.其次,证明了恒等式x^n≈x加法幂等元半环簇的所有局部有限成员的类作成簇,从而回答了该簇的限制Burnside问题.最后,给出了相关文献的主要结果的一个简洁证明.This paper proves that if an additively idempotent semiring is inherently non finitely based,so is its multiplicative reduct.As an application,we show that every finite additively idempotent semiring whose cardinality is less than seven or satisfying x^n≈x is not inherently nonfinitely based.Also,we show that the class of all locally finite members of the additively idempotent semiring variety defined by x^n≈x forms a variety.Finally,we provide a simple proof for the main result of relation.

关 键 词：加法幂等元半环 簇 遗传非有限基底 局部有限 

分 类 号：O153.5[理学—数学]