Goldie M-groups

Journal of the Australian Mathematical Society

K. C. Chowdhury¹ 

关键词: 16 A 34;    16 A 76;    20 B 99;   

DOI  :  10.1017/S1446788700034212

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

If (G+) is a group and M is a nonempty set of endomorphisms of G operating on the left then G is said to be M-Goldie when (i) G has no infinite independent family of nonzero M-subgroups, and (ii) annihilators in M of subsets of G satisfy the a.c.c. (under set inclusion). Here we prove some results, analogous to those of a Noetherian module in some special cases, even when the set M of operators has no other algebraic structure than the existence of a zero element or in some cases M is at most a finite dimensional commutative near-ring. Precisely speaking, we prove that the collection of associated operating sets of G is finite and there exists a primary decomposition of 0 of such a Goldie M-group, and then if M is a finite dimensional commutative near-ring with unity, for any x belonging to each associated operating set of G, a power of it belongs to the annthilator of G.

【 授权许可】

Unknown