A scheme associated to modules over commutative rings

被引：0

作者：

Parsa, Mohammad Ali ^{[1
]}

Moghimi, Hosein Fazaeli ^{[1
]}

机构：

[1] Univ Birjand, Dept Math, POB 97175-615, Birjand, Iran

来源：

COMMUNICATIONS IN ALGEBRA | 2024年 / 52卷 / 12期

关键词：

Affine scheme; morphism of schemes; prime submodule; scheme; sheaf; PRIME SPECTRUM; SHEAF;

D O I：

10.1080/00927872.2024.2369150

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For any module M over a commutative ring R with identity, we consider Sch(M) as a certain class of prime submodules modulo the equivalence relation that two such prime submodules are the same if their colon ideals are equal. We topologize Sch(M) and introduce a sheaf OSch(M) of commutative rings on it, which makes (Sch(M),OSch(M)) into a scheme. In particular, if M is a module over a Noetherian ring R, then (Sch(M),OSch(M)) is a locally Noetherian scheme. Among others, we give sufficient conditions for Sch(M) to be an affine scheme.

引用

页码：5289 / 5301

页数：13

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