Category of Generalized Modules Over Two Different Rings

Authors

  • Tariq Z. Al-Killabi Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Jadriya, Baghdad, Iraq
  • Hassan J. Al-Hwaeer Ministry of Higher Education and Scientific Research, Baghdad, Iraq
  • Ali A. Al-Butahi Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Jadriya, Baghdad, Iraq

Keywords:

Generalized modules, Enriched categories, Grothendieck categories, Commutative Rings

Abstract

In this paper, a method of enriched category theory to form a closed symmetric monoidal structure on the category of generalized modules CR = (mod R,Ab) have been implemented. Further, a new kind of generalized module category defined on two commutative rings R and S, denoted by CRS = (mod R,mod S) is constructed. Finally, the authors studied a localization on this type of categories, both of them are Grothendieck.

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Published

2023-04-03

Issue

Vol. 26 No. 1 (2023): March

Section

Mathematics

How to Cite

(1)
Z. Al-Killabi, T.; J. Al-Hwaeer, H.; A. Al-Butahi, A. Category of Generalized Modules Over Two Different Rings. Al-Nahrain J. Sci. 2023, 26 (1), 31-40.