Cancellation elements in multiplicative lattices
We extend to multiplicative lattices a theorem of Anderson and Roitman characterizing the cancellation ideals of a commutative ring.
math.AC↗
arXiv subjects
Tiberiu Dumitrescu
Publications and source records attributed to Tiberiu Dumitrescu.
Divisorial Multiplicative Lattices
We prove several fundamental results about divisorial integral domains in the setup of multiplicative lattices.
math.AC↗
Lifting multiplicative lattices to ideal sytems
We present a mechanism which lifts a multiplicative lattice to a (weak) ideal system on some monoid.
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Kaplansky/Nagata-type theorems for the half factorial domains
We give Kaplansky/Nagata-type theorems for the half factorial domains inside the class of atomic domains.
math.AC↗
A Schreier type property for modules
We extend to torsion-free modules over integral domains the theory of (pre)-Schreier domains initiated by Cohn and Zafrullah.
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psi-morphisms
We extend to ring morphisms the recent work of Mohamed Khalifa on PSI-extensions.
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Comaximal Factorization Lattices
Brewer and Heinzer studied the (integral) domains D having the property that each proper ideal A of D has a comaximal ideal factorization with some additional property. They proved that for a domain D, the following are equivalent: (1) Each proper ideal A of D has a comaximal factorization where the factors have prime radical (resp. are primary, resp. are prime powers). (2) The prime spectrum of D is a tree under inclusion and each ideal of D has only finitely many minimal primes (resp. D is one dimensional and each ideal of D has only finitely many minimal primes, resp. D is a Dedekind domain). The aim of this paper is to show that most of the results can be obtained in the setup of multiplicative lattices.
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A locally F-finite Noetherian domain that is not F-finite
Using an old example of Nagata, we construct a Noetherian ring of prime characteristic p, whose Frobenius morphism is locally finite, but not finite.
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A class of multiplicative lattices
We study the multiplicative lattices L which satisfy the condition a = (a : (a : b))(a : b) for all a,b in L.
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Domains with invertible-radical factorization
We study those integral domains in which every proper ideal can be written as an invertible ideal multiplied by a nonempty product of proper radical ideals.
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Commutative Rings with Two-Absorbing Factorization
We use the concept of 2-absorbing ideal introduced by Badawi to study those commutative rings in which every proper ideal is a product of 2-absorbing ideals (we call them TAF-rings). Any TAF-ring has dimension at most one and the local TAF-domains are the atomic pseudo-valuation domains.
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SP-rings with zero-divisors
We characterize the commutative rings whose ideals (resp. regular ideals) are products of radical ideals.
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Perinormal rings with zero divisors
We extend to rings with zero-divisors the concept of perinormal domain introduced by N. Epstein and J. Shapiro. A ring $A$ is called perinormal if every overring of $A$ which satisfies going down over $A$ is $A$-flat. The Prüfer rings and the Marot Krull rings are perinormal.
math.AC↗
A note on perinormal domains
Recently, N. Epstein and J. Shapiro introduced and studied the perinormal domains: those domains A whose going down overrings are flat A-modules. We show that every Prüfer v-multiplication domain is perinormal and has no proper lying over overrings. We also show that a treed perinormal domain is a Prüfer domain. We give two pull-back constructions that produce perinormal/non-perinormal domains.
math.AC↗
Some examples of two-dimensional regular rings
Let B be a ring and $A=B[X,Y]/(aX^2+bXY+cY^2-1)$ where $a,b,c\in B$. We study the smoothness of A over B, and the regularity of B when B is a ring of algebraic integers.
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A Schreier domain type condition II
For an integral domain D and a star operation * on D, we study the following condition: whenever I>AB with I, A, B nonzero ideals, there exist nonzero ideals H and J such that I*=(HJ)*, H*>A and J*>B.
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A Schreier Domain Type Condition
We study the integral domains D satisfying the following condition: whenever I >AB with I,A,B nonzero ideals, there exist ideals A'>A and B'>B such that I=A'B'.
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Generic fiber of power series ring extensions
Let D be a Noetherian domain containing a field, d a nonzero nonunit of D and z an indeterminate over D. We prove that the generic fiber of D[1/d][[z]] over D[[z]] has dimension greater than the dimension of D/dD.
math.AC↗