Related papers: Cubic rings and their ideals
In this paper, we introduce the concept of n-semiprimary ideals, n-powerful ideals, and n-powerful semiprimary ideals of commutative rings. We study these concepts and relate them to several generalizations of pseudo-valuation domains.
In this exposition-type note we present detailed proofs of certain assertions concerning several algebraic properties of the cone and cylinder algebras. These include a determination of the maximal ideals, the solution of the B\'ezout…
In this study, we introduce the concept of "uniformly 2-absorbing primary ideals" of commutative rings, which imposes a certain boundedness condition on the usual notion of 2-absorbing primary ideals of commutative rings. Then we…
Primary hyperideals have been introduced and studied in multiplicative hyperrings. In this paper, we intend to study extensively primary hyperideals of multiplicative hyperrings with absorbing zero and prove some results regarding them.…
The aim of this series of papers is to study $z$-ideals of semirings. In this article, we introduce some distinguished classes of $z$-ideals of semirings, which include $z$-prime, $z$-semiprime, $z$-irreducible, and $z$-strongly irreducible…
There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent to the classical notion within classical mathematics, and…
This paper considers graded near-rings over a monoid G as a generalizations of the graded rings over groups, introduce certain innovative graded weakly prime ideals and graded almost prime ideals as a generalizations of graded prime ideals…
The present paper studies structure of the ring of integer-valued entire functions. We characterize certain classes of prime and maximal ideals and investigate some of their properties.
In this paper we introduce the notion of "strong $n$-perfect rings" which is in some way a generalization of the notion of "$n$-perfect rings". We are mainly concerned with those class of rings in the context of pullbacks. Also we exhibit a…
We introduce the concept of constructible ideal and we relate this concept with the notion of constructible simplicial complex. Several properties of constructible ideals are studied.
In this paper, we introduce the concept of N-pure ideal as a generalization of pure ideal. Using this concept, a new and interesting type of rings is presented, we call it mid ring. Also, we provide new characterizations for von Neumann…
Can there be a structure space-type theory for an arbitrary class of ideals of a ring? The ideal spaces introduced in this paper allows such a study and our theory includes (but not restricted to) prime, maximal, minimal prime, strongly…
In [1], finite associative rings wih identity and such that the set of all zero-divisors form and ideal M, called the Jacobson Radical, of cube zero and square non-zero, were constructed for all the characteristics. These rings are…
In this paper, we give a detailed proof to a result of Gabber (unpublished) on the lifting problem of quasi-excellent rings, extending the previous work on Nishimura-Nishimura. As a corollary, we establish that an ideal-adic completion of…
In this paper, we give a complete description of the complex and the real Waring ranks of reducible cubic forms over C.
We consider a convenient category of "quadratic" multirings, that allows simple functorial relations with categories associated with abstract quadratic forms theories and shares many good aspects of the theories of Special Groups and of…
In this paper we show that if R is a discrete valuation ring, then R is a filtered ring. We prove some properties and relation when R is a discrete valuation ring.
This article investigates various notions of primeness for one-sided ideals in noncommutative rings, with a focus on principal ideal domains.
In this note, finite type epimorphisms of rings are characterized.
We study well-rounded ideal lattices from totally definite quaternion algebras. We prove existence and classification results, and illustrate our methods with examples.