In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study weakly prime ideals. We investigate rings in which all graded...

In recent work of T. Cassidy and the author, a notion of complete intersection was defined for (non-commutative) regular skew polynomial rings, defining it using both algebraic and geometric tools, where the commutative definition is a special case. In this article, we extend the definition to a larger class of algebras that contains regular graded skew Clifford algebras, the coordinate ring of...

A ring is a set R with two binary operations usually called addition, denoted as +, and multiplication, denoted as ·, such that (R, +) satisfies the five axioms of closure, associativity, commutativity, identity element (called zero, 0), and inverse element; and (R, ·) satisfies the three axioms of closure, associativity, and identity element (called one, 1). Furthermore, multiplication (·) dis...

A ring is called a Gelfand ring (pm ring ) if each prime ideal is contained in a unique maximal ideal. For a Gelfand ring R with Jacobson radical zero, we show that the following are equivalent: (1) R is Artinian; (2) R is Noetherian; (3) R has a finite Goldie dimension; (4) Every maximal ideal is generated by an idempotent; (5) Max (R) is finite. We also give the following resu1ts:an ideal...

In this paper, we describe all automorphism-liftable torsion modules over non-primitive hereditary Noetherian prime rings. We also study non-torsion not necessarily commutative Dedekind