AbstractThe main theorem of this article is an extension of the generalized principal ideal theorem for ideals in Noetherian rings. Instead of requiring the rings to be Noetherian, some natural requirements are imposed on the chains of prime ideals under consideration. The standard (Noetherian) version of the generalized principal ideal theorem is deduced as a corollary and two other applications are presented
An ideal in a polynomial ring encodes a system of linear partial differential equations with constan...
This thesis is concerned with understanding the prime ideal structure in certain classes of commutat...
Abstract. Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime...
AbstractThe main theorem of this article is an extension of the generalized principal ideal theorem ...
We introduce primary ideals and prove the Lasker-Noether theorem, namely that in a noetherian ring a...
A ring is called an r-Noetherian ring if every regular ideal is finitely generated. Let R be an r-No...
Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying...
Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying...
AbstractThis article introduces and advances the basic theory of “uniformly primary ideals” for comm...
Recent work toward extending the theory of Cohen-Macaulayness to all commutative rings (both Noether...
the concept of a principal ideal in a ring to a principal element in a lattice. He then used princiv...
Abstract. For a regular ideal having a principal reduction in a Noetherian ring we consider the stru...
Let be a group and is a ring. be a graded ring if and for all , . The elements of are called homogen...
The concepts of prime ideals and prime modules were introduced over noncommutative rings. In this ar...
In this paper we look at the properties of modules and prime ideals in finite dimensional noetherian...
An ideal in a polynomial ring encodes a system of linear partial differential equations with constan...
This thesis is concerned with understanding the prime ideal structure in certain classes of commutat...
Abstract. Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime...
AbstractThe main theorem of this article is an extension of the generalized principal ideal theorem ...
We introduce primary ideals and prove the Lasker-Noether theorem, namely that in a noetherian ring a...
A ring is called an r-Noetherian ring if every regular ideal is finitely generated. Let R be an r-No...
Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying...
Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying...
AbstractThis article introduces and advances the basic theory of “uniformly primary ideals” for comm...
Recent work toward extending the theory of Cohen-Macaulayness to all commutative rings (both Noether...
the concept of a principal ideal in a ring to a principal element in a lattice. He then used princiv...
Abstract. For a regular ideal having a principal reduction in a Noetherian ring we consider the stru...
Let be a group and is a ring. be a graded ring if and for all , . The elements of are called homogen...
The concepts of prime ideals and prime modules were introduced over noncommutative rings. In this ar...
In this paper we look at the properties of modules and prime ideals in finite dimensional noetherian...
An ideal in a polynomial ring encodes a system of linear partial differential equations with constan...
This thesis is concerned with understanding the prime ideal structure in certain classes of commutat...
Abstract. Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime...
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