Different and distinct notions of regularity for modules exist in the literature. When these
notions are restricted to commutative rings, they all coincide with the well-known von …

This is the first in a series of papers highlighting the applications of reduced and coreduced
modules. Let $ R $ be a commutative unital ring and $ I $ be an ideal of $ R $. We show that …

Let R be a commutative unital ring, a ∈ R a∈ R and ta positive integer. a^ t at-reduced R-
modules and universally a^ t at-reduced R-modules are defined and their properties given …

Let $ A $ be a commutative unital ring. We prove the MGM equivalence and the Greenless-
May duality in the category of chain complexes of $ A $-modules. This extends the above …

Let $ R $ be a commutative unital ring, $\mathfrak {a} $ an ideal of $ R $ and $ M $ a fixed $
R $-module. We introduce and study generalisations of $\mathfrak {a} $-reduced modules …

Let $ k $ be a field with characteristic zero, $ R $ be the ring $ k [x_1,\cdots, x_n] $ and $ I $
be a monomial ideal of $ R $. We study the Artinian local algebra $ R/I $ when considered …

Let A be a commutative unital ring. We prove the MGM equivalence and the Greenless-May
duality in the category of chain complexes of A-modules. This extends the above notions …

In this dissertation, we study the relationships between the notions of a morphic element and
a morphic ring or module on one hand and reduced and regular rings or modules on the …