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
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
收藏
页码:5289 / 5301
页数:13
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