Topics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of ...

ABSTRACT. We study the relationship between algebras generated by idempotents over a commutative ring 𝑅 with identity and algebras that are quotient rings of group algebras 𝑅𝐺 for torsion abelian ...

ABSTRACT. The concept of Gorenstein dimension, defined by Auslander and Bridger for finitely generated modules over a Noetherian ring, is studied in the context of finitely presented modules over a ...

Commutative algebra and graph theory are two vibrant areas of mathematics that have grown increasingly interrelated. At this interface, algebraic methods are applied to study combinatorial structures, ...

Algebraic structures provide a comprehensive framework for understanding systems governed by operations such as addition and multiplication. In this context, noncommutative rings—where the order of ...