Let R be a commutative ring with nonzero identity and Γ (or sometimes G) a commutative
monoid. The concept of coherent rings is one of the most significant notions in homological …

This book provides the first extensive and systematic treatment of the theory of commutative
coherent rings. It blends, and provides a link, between the two sometimes disjoint …

The study of rings and modules with homological criteria is a cornerstone of commutative
algebra. Let $ R $ be a commutative Noetherian ring with identity (not necessarily local) and …

This book provides the first extensive and systematic treatment of the theory of commutative
coherent rings. It blends, and provides a link, between the two sometimes disjoint …

Let $ R=\oplus_ {\alpha\in G} R_ {\alpha} $ be a commutative ring with unity graded by an
arbitrary grading commutative monoid $ G $. For each positive integer, the notions of a …

Let R be a commutative ring with identity. The main purpose of this paper is to introduce the
notions of comultiplication-like and virtually codivisible R-modules as generalizations of …

This paper unifies several generalizations of coherent rings in one notion. Namely, we
introduce nX-coherent rings, where X is a class of modules and n is a positive integer, as …

Let A= ⊕ _ α ∈ G A_ α A=⊕ α∈ GA α be a commutative ring with unity graded by an
arbitrary grading commutative monoid G, E be a graded A-module and R= A ∝ ER= A∝ E …

Some properties of graded comultiplication modules Skip to content Should you have
institutional access? Here's how to get it ... De Gruyter € EUR - Euro £ GBP - Pound $ USD …

Graded Injective Modules and Graded Quasi-Frobenius Rings 0 Introduction Page 1
Applied Mathematical Sciences, Vol. 9, 2015, no. 23, 1113 - 1123 HIKARI Ltd, www.m-hikari.com …