COHERENCY AND CONSTRUCTIONS FOR MONOIDS
COHERENCY AND CONSTRUCTIONS FOR MONOIDS
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DOI：
10.1093/qmath/haaa040
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发表时间：
2020-12-01
影响因子：
0.7
通讯作者：
Zenab, Rida-E
中科院分区：
文献类型：
--
作者：
Dandan, Yang;Gould, Victoria;Zenab, Rida-E
一个么半群是右凝聚的，如果每个有限表示的右S-系的每个有限生成子系都是有限表示的。这是一个有限的条件，我们考察了它在一些标准的代数和半群理论构造下是否保持：子半群、同态像、直积、Rees矩阵半群，包括Brandt半群和Bruck-Reilly扩张。我们还研究了它与弱右Notherian性质的关系，这要求S的所有右理想都是有限生成的。
A monoid S is right coherent if every finitely generated subact of every finitely presented right S-act is finitely presented. This is a finiteness condition, and we investigate whether or not it is preserved under some standard algebraic and semigroup theoretic constructions: subsemigroups, homomorphic images, direct products, Rees matrix semigroups, including Brandt semigroups, and Bruck-Reilly extensions. We also investigate the relationship with the property of being weakly right noetherian, which requires all right ideals of S to be finitely generated.