On graded coherent-like properties in trivial ring extensions

Assarrar A., Mahdou N., Tekir Ü., Koç S.

BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1007/s40574-021-00312-6
  • Journal Name: BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA
  • Journal Indexes: Emerging Sources Citation Index, Scopus, L'Année philologique, MathSciNet, zbMATH, DIALNET
  • Keywords: Graded trivial extension, Trivial extension, Graded modules and rings, Coherent rings and modules, Graded-v-coherence, MODULES

Abstract

Let A = circle plus(alpha is an element of G) A(alpha) be a commutative ring with unity graded by an arbitrary grading commutative monoid G, E be a graded A-module and R = A proportional to E the graded trivial extension. In this paper, in the second section, we improve some results on graded trivial extension and we give some new ones and the theme throughout is how homogeneous properties are related to those of A and E. Then, in another section, we introduce and study the notions of graded-v-coherent, graded-quasi-coherent and graded-finite conductor rings, then we study their transfer in the graded trivial extension.