Results 1 to 10 of about 397,514 (346)
On S-principal right ideal rings
AIMS Mathematics, 2022 Let S be a multiplicative subset of a ring R. A right ideal A of R is referred to as S-principal if there exist an element s∈S and a principal right ideal aR of R such that As⊆aR⊆A.
Jongwook Baeck
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Similarity Classes of 3 × 3 Matrices Over a Local Principal Ideal Ring [PDF]
, 2009 In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is ...
Nir Avni +3 more
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On QF rings and artinian principal ideal rings
Hacettepe Journal of Mathematics and Statistics, 2017 Summary: In this work we give sufficient conditions for a ring \(R\) to be quasi-Frobenius, such as \(R\) being left artinian and the class of injective cogenerators of \(R\)-Mod being closed under projective covers. We prove that \(R\) is a division ring if and only if \(R\) is a domain and the class of left free \(R\)-modules is closed under ...
Alejandro Alvarado-García +4 more
semanticscholar +5 more sources
Prime Principal Right Ideal Rings [PDF]
Missouri Journal of Mathematical Sciences, 2022 Let R be a commutative ring with unity $1\in R$. In this article, we introduce the concept of prime principal right ideal rings (\textbf{PPRIR}), A prime ideal P of R is said to be prime principal right ideal (\textbf{PPRI}) is given by $P =\{ ar : r\in R\}$ for some element a.
Tamem Al-Shorman, Malik Bataineh
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When is R[x] a principal ideal ring?
Revista Integración, 2018 Because of its interesting applications in coding theory, cryptography, and algebraic combinatoris, in recent decades a lot of attention has been paid to the algebraic structure of the ring of polynomials R[x], where R is a finite commutative ring with ...
Henry Chimal-Dzul, C. A. López-Andrade
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Morphic and principal-ideal group rings [PDF]
Journal of Algebra, 2007 We observe that the class of left and right artinian left and right morphic rings agrees with the class of artinian principal ideal rings. For $R$ an artinian principal ideal ring and $G$ a group, we characterize when $RG$ is a principal ideal ring; for finite groups $G$, this characterizes when $RG$ is a left and right morphic ring.
Thomas J. Dorsey
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A class of principal ideal rings arising from the converse of the Chinese remainder theorem [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 Let R be a (nonzero commutative unital) ring. If I and J are ideals of R such that R/I⊕R/J is a cyclic R-module, then I+J=R. The rings R such that R/I⊕R/J is a cyclic R-module for all distinct nonzero proper ideals I and J of R are the following three ...
David E. Dobbs
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Finite local principal ideal rings [PDF]
, 2023 Every finite local principal ideal ring is the homomorphic image of a discrete valuation ring of a number field, and is determined by five invariants. We present an action of a group, non-commutative in general, on the set of Eisenstein polynomials, of degree matching the ramification index of the ring, over the coefficient ring.
Matthé van der Lee
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On the structure of principal ideal rings [PDF]
Pacific Journal of Mathematics, 1968 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Thomas W. Hungerford
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Rings with Every Proper Image a Principal Ideal Ring [PDF]
Proceedings of the American Mathematical Society, 1981 The main result of this paper states that if R is a right Noetherian right bounded prime ring such that nonzero prime ideals are maximal and such that every proper homomorphic image of R is a principal right ideal ring then R is right hereditary. In [10, Theorem 8] it is proved that if R is a right bounded prime ring of finite right Goldie dimension ...
P. F. Smith
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