This book contains the definitions of several ring constructions used in various applications.
The concept of a groupoid-graded ring includes many of these constructions as special …

NOETHERIAN SEMIGROUP ALGEBRAS Page 1 Bull. London Math. Soc. 38 (2006) 421–428 C
2006 London Mathematical Society doi:10.1112/S0024609305018357 NOETHERIAN …

Let R=⊕ α∈ Γ R α be an integral domain graded by an arbitrary torsionless grading monoid
Γ. We say that R is a graded Prüfer domain if every nonzero finitely generated …

Let $ D $ be an integral domain with quotient field $ K $, $ X $ be an indeterminate over $ D
$, $ K [X] $ be the polynomial ring over $ K $, and $ R=\{f\in K [X]\mid f (0)\in D\} $; so $ R $ is …

Recently. many authors have been interested in m~ iltiplication modules and rings (cf.
171,[8],[16],[20] and their references). Hereditary rings, von Neumann regular rings and …

Abstract Let A⊆ B be an extension of integral domains, X be an indeterminate over B, and
R= A+ XB [X]. We prove that if B is t-flat over A, then R is a PvMD if and only if A is a PvMD …

Let R=⊕ α∈ Γ R α be an integral domain graded by a nontrivial torsionless grading monoid
Γ. Among other things, we show that if Γ∩(− Γ)={0}, then every nonzero homogeneous ideal …

The main aim of this book is to study the concept of multiplication objects from a categorical
point of view, namely, in the setting of monoidal categories which are responsible for the …

Let D be an integral domain and w be the so-called w-operation on D. In this paper, we
define the notion of w-ZPUI domains which is a natural generalization of ZPUI domains …

Natural classes of Noetherian rings include enveloping algebras of finite dimensional Lie
algebras, crossed product algebras of polycyclic-by-finite groups and finitely generated …