Explanipedia

Divisorial Multiplicative Lattices Open

Tiberiu Dumitrescu, Mihai Epure · 2025

We prove several fundamental results about divisorial integral domains in the setup of multiplicative lattices.

Lifting multiplicative lattices to ideal sytems Open

Tiberiu Dumitrescu, Mihai Epure, Alexandru Gica · 2024

We present a mechanism which lifts a multiplicative lattice to a (weak) ideal system on some monoid.

Kaplansky/Nagata-type theorems for the half factorial domains Open

Tiberiu Dumitrescu · 2023

We give Kaplansky/Nagata-type theorems for the half factorial domains inside the class of atomic domains.

A locally F-finite Noetherian domain that is not F-finite Open

Tiberiu Dumitrescu, Cristodor Ionescu · 2022

Using an old example of Nagata, we construct a Noetherian ring of prime characteristic p, whose Frobenius morphism is locally finite, but not finite.

A Schreier type property for modules Open

Tiberiu Dumitrescu, Mihai Epure · 2022

We extend to torsion-free modules over integral domains the theory of (pre)-Schreier domains initiated by Cohn and Zafrullah.

psi-morphisms. Open

Tiberiu Dumitrescu, Mihai Epure · 2021

psi-morphisms Open

Tiberiu Dumitrescu, Mihai Epure · 2021

We extend to ring morphisms the recent work of Mohamed Khalifa on PSI-extensions.

Comaximal Factorization Lattices Open

Tiberiu Dumitrescu, Mihai Epure · 2021

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) Eac…

A class of multiplicative lattices Open

Tiberiu Dumitrescu, Mihai Epure · 2021

We study the multiplicative lattices L which satisfy the condition a = (a : (a : b))(a : b) for all a,b in L.

A locally F-finite Noetherian domain that is not F-finite Open

Tiberiu Dumitrescu, Cristodor Ionescu · 2020

Using an old example of Nagata, we construct a Noetherian ring of prime characteristic p, whose Frobenius morphism is locally finite, but not finite.

Perinormal polynomial domains Open

Tiberiu Dumitrescu, Anam Rani · 2018

Let A be a domain. We relate the perinormality (as dened byEpstein and Shapiro) of A and A[X] for a narrow class of Noetherian domains.

Commutative rings with two-absorbing factorization Open

Muzammil Mukhtar, Malik Tusif Ahmed, Tiberiu Dumitrescu · 2017

We use the concept of 2-absorbing ideal introduced by Badawi to study those\ncommutative rings in which every proper ideal is a product of 2-absorbing\nideals (we call them TAF-rings). Any TAF-ring has dimension at most one and the\nlocal …

Domains with invertible-radical factorization Open

Malik Tusif Ahmed, Tiberiu Dumitrescu · 2016

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.

Perinormal rings with zero divisors Open

Tiberiu Dumitrescu, Anam Rani · 2016

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 …

A note on perinormal domains Open

Tiberiu Dumitrescu, Anam Rani · 2015

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 …

A Schreier Domain Type Condition II Open

Zaheer Ahmad, Tiberiu Dumitrescu, Mihai Epure · 2015

Let D be an integral domain and ∗ a star operation on D. We study the domains characterized by the following property: whenever I ⊇ AB with I, A, B nonzero ideals, there exist nonzero ideals H and J such that I ∗ = (HJ) ∗ , H ∗ ⊇ A and J ∗…

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