English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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  s  ∈  S  such that for all nonunit elements  a, b, c  ∈  A  such that  abc  ∈  I  (resp. 0 ≠  abc  ∈  I ), we have  sab  ∈  I  or  sc  ∈  I . 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.

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