107
Views
0
CrossRef citations to date
0
Altmetric
Research Article

On S-1-absorbing prime and weakly S-1-absorbing prime ideals

, &
Pages 101-115 | Received 14 Jun 2021, Published online: 18 Jan 2022
 

Abstract

Let A be a commutative ring with identity and S be a multiplicative subset of A. In this paper, we introduce and study the notions of S-1-absorbing and weakly S-1-absorbing prime ideals as generalizations of the notion of prime ideals. We define a proper ideal I disjoint with S to be an S-1-absorbing (resp. a weakly S-1-absorbing) prime ideal if there exists sS such that for all nonunit elements a, b, cA such that abcI (resp. 0 ≠ abcI), we have sabI or scI. Several properties and characterizations of S-1-absorbing prime and weakly S-1-absorbing prime ideals are given. Moreover, we study the transfer of the above properties to some constructions of rings such as trivial ring extensions and amalgamation of rings along an ideal.

Mathematics Subject Classification (2020):

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.