Results 31 to 40 of about 326,550 (311)
Essentially iso-retractable modules and rings
Karpatsʹkì Matematičnì Publìkacìï, 2022 A.K. Chaturvedi et al. (2021) call a module $M$ essentially iso-retractable if for every essential submodule $N$ of $M$ there exists an isomorphism $f : M\rightarrow N.$ We characterize essentially iso-retractable modules, co-semisimple modules ($V ...
A.K. Chaturvedi +3 more
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On Commutative Rings Whose Prime Ideals Are Direct Sums of Cyclics [PDF]
, 2012 In this paper we study commutative rings $R$ whose prime ideals are direct sums of cyclic modules. In the case $R$ is a finite direct product of commutative local rings, the structure of such rings is completely described. In particular, it is shown that
Behboodi, Mahmood +1 more
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Classification of Rings with Toroidal and Projective Coannihilator Graph
Journal of Mathematics, 2021 Let S be a commutative ring with unity, and a set of nonunit elements is denoted by WS. The coannihilator graph of S, denoted by AG′S, is an undirected graph with vertex set WS∗ (set of all nonzero nonunit elements of S), and α∼β is an edge of AG′S⇔α∉αβS
Abdulaziz M. Alanazi +2 more
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Mathematics, 2021 The purpose of this paper is to introduce the concept of graded 2-prime ideals as a new generalization of graded prime ideals. We show that graded 2-prime ideals and graded semi-prime ideals are different.
Malik Bataineh, Rashid Abu-Dawwas
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Null ideals of matrices over residue class rings of principal ideal domains [PDF]
, 2016 Given a square matrix $A$ with entries in a commutative ring $S$, the ideal of $S[X]$ consisting of polynomials $f$ with $f(A) =0$ is called the null ideal of $A$. Very little is known about null ideals of matrices over general commutative rings.
Rissner, Roswitha
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On matrices with elements in a principal ideal ring [PDF]
Bulletin of the American Mathematical Society, 1949 We prove the following theorem: Let D be any commutative principal ideal ring without divisors of zero, and A any matrix with elements in D whose characteristic equation factors into linear factors in D. Then there exists a unimodular matrix T, with elements in D, such that T–1 AT has zeros below the main diagonal.
Leavitt, William, Whaples, George
openaire +2 more sources
关于右GP-V-环(On right GP-V-rings)
Zhejiang Daxue xuebao. Lixue ban, 2009 GP-V-ring(GP-V-module) is studied which is a generalization of P-V-ring (P-V-module), and the characters are searched for. For example,if R is a right GP-V-ring, then for any maximal subideal K of a principal right ideal U= aR, a ∈R, there exists a ...
YANGChun-lan(杨春兰)
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On weakly S-prime ideals of commutative rings
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Let R be a commutative ring with identity and S be a multiplicative subset of R. In this paper, we introduce the concept of weakly S-prime ideals which is a generalization of weakly prime ideals. Let P be an ideal of R disjoint with S. We say that P is a
Almahdi Fuad Ali Ahmed +2 more
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On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
Mathematics, 2021 In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings.
Ángel Luis Muñoz Castañeda +2 more
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Projective prime ideals and localisation in pi-rings [PDF]
, 2001 The results here generalise [2, Proposition 4.3] and [9, Theorem 5.11]. We shall prove the following. THEOREM A. Let R be a Noetherian PI-ring. Let P be a non-idempotent prime ideal of R such that PR is projective. Then P is left localisable and RP is
Chatters, A. W. +2 more
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