Results 151 to 160 of about 30,364 (194)

U-factorization of ideals

Communications in Algebra, 2018
AbstractWe study the factorization of ideals of a commutative ring, in the context of the U-factorization framework introduced by Fletcher.
Jason Robert Juett, Christopher Park Mooney   +1 more
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Factoring Nonnil Ideals into Prime and Invertible Ideals

Bulletin of the London Mathematical Society, 2005
Throughout all rings are commutative with non-zero identity. For a ring \(R\), let \(\text{ Nil}(R)\) be its set of nilpotent elements, \(Z(R)\) its set of zero divisors and \(T(R)\) the total quotient ring of \(R\). Let \(\mathcal{H}\) be the class of all rings \(R\) such that \(\text{ Nil}(R)\) is a divided prime ideal of \(R\). For \(R\in \mathcal{H}
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Comaximal factorization of lifting ideals

Journal of Algebra and Its Applications, 2020
A proper ideal [Formula: see text] of a commutative ring [Formula: see text] is called lifting whenever idempotents of [Formula: see text] lift to idempotents of [Formula: see text]. In this paper, many of the basic properties of lifting ideals are studied and we prove and extend some well-known results concerning lifting ideals and lifting ...
Rostami, Esmaeil, Hedayat, Sina, Nekooei, Reza, Karimzadeh, Somayeh   +3 more
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Factoring Ideals in Integral Domains

2013
A classical generalization of the Fundamental Theorem of Arithmetic states that an integral domain is a principal ideal domain if and only if each of its proper ideals can be factored as a finite product of principal prime ideals. If the “principal” restriction is removed, one has a characterization of (nontrivial) Dedekind domains. The purpose of this
FONTANA, Marco, Houston, Evan, Lucas, Thomas   +2 more
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Ideally factored algebras

2008
Summary: A complex algebra \(\mathcal A\) is called ideally factored if \(\mathcal I_a=\mathbb C a\) is a left ideal of \(\mathcal A\) for all \(a \in \mathcal A\). We investigate some interesting properties of ideally factored algebras and show that these algebras are always Arens regular but never amenable.
Amyari, M., Mirzavaziri, M.
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Factorization into Prime and Invertible Ideals

Journal of the London Mathematical Society, 2000
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Unique Factorization Domains, Ideals, and Principal Ideal Domains

2001
Let A be a domain, that is, a commutative ring with unit element (different from 0), having no zero-divisors (except 0). Let K be its field of quotients.
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Homomorphisms, ideals, and factor rings

1998
Abstract It is often the case that two rings for which we already have some information are in fact related to each other. For instance the ring 71./nl of integers mod n is in some sense derived from the ring 71. of integers. We shall now study such connections between rings.
A W Chatters, C R Hajarnavis
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Missing Factors of Ideals and Synchronizing Automata

2019
Recently, a series of papers have started to look at \v{C}ern\'y's conjecture, and in general at synchronizing automata, from the point of view of the theory of ideals of free monoids. The starting point of such an approach is a simple observation: the set of reset words of an automaton is a two-sided ideal of the free monoid on its alphabet that is ...
Frigeri A., Rodaro E.
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Asymptotic Factorization of Ideals

Journal of the London Mathematical Society, 1963
Muhly, H. T., Sakuma, M.
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