Results 241 to 250 of about 3,388 (272)

Triangular matrix rings of selfinjective rings

Communications in Algebra, 2020
A module M is said to be generalized extending if for every submodule N≤M there exists a direct summand D of M containing N such that D/N is a singular module.
M. Zahiri, A. Moussavi, R. Mohammadi
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ON GENERALIZED TRIANGULAR MATRIX RINGS [PDF]

East Asian Mathematical Journal, 2014
For a generalized triangular matrix ring T = R M 0 S , over rings R and S having only the idempotents 0 and 1 and over an (R;S)-bimodule M, we characterize all homomorphisms 's and all - derivations of T. Some of the homomorphisms are compositions of an inner homomorphism and an extended or a twisted homomorphism.
Jang Ho Chun, June Won Park
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On reduced rank of triangular matrix rings

Journal of Algebra and Its Applications, 2015
We determine conditions under which a generalized triangular matrix ring has finite reduced rank, in the general torsion-theoretic sense. These are applied to characterize certain orders in Artinian rings, and to show that if each homomorphic image of a ring S has finite reduced rank, then so does the ring of lower triangular matrices over S.
Bailey, Abigail C., Beachy, John A.
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On Strongly Clean Matrix and Triangular Matrix Rings

Communications in Algebra, 2006
A ring R with identity is called “clean” if every element of R is the sum of an idempotent and a unit, and R is called “strongly clean” if every element of R is the sum of an idempotent and a unit that commute. Strongly clean rings are “additive analogs” of strongly regular rings, where a ring R is strongly regular if every element of R is the product ...
Jianlong Chen, Xiande Yang, Yiqiang Zhou
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Idempotents in triangular matrix rings

Linear and Multilinear Algebra, 2019
Let R be an associative ring with identity 1. We describe all idempotent matrices with only zeros and ones on the diagonal in T(n,R) – the ring of n×n upper triangular matrices over R (n∈N), and T(...
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On Skew Triangular Matrix Rings

Communications in Algebra, 2011
For a ring R, endomorphism α of R and positive integer n we define a skew triangular matrix ring T n (R, α). By using an ideal theory of a skew triangular matrix ring T n (R, α) we can determine prime, primitive, maximal ideals and radicals of the ring R[x; α]/ ⟨ x n  ⟩, for each positive integer n, where R[x; α] is the skew polynomial ring, and ⟨ x n  
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Endomorphisms of upper triangular matrix rings

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On skew generalized triangular matrix rings

Summary: In this article, we study skew monoid rings in which the monoid used in their structure is a quotient of a free monoid. We study annihilator conditions of them and describe conditions for transferring some properties from the base ring \(R\) to these extensions. Interesting examples are provided for properties that are not transferred from \(R\
Habibi, Mohammad, Paykan, Kamal
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Quasipolar Triangular Matrix Rings Over Local Rings

Communications in Algebra, 2012
A ring R is quasipolar if for any a ∈ R, there exists p 2 = p ∈ R such that , a + p ∈ U(R) and ap ∈ R qnil . In this article, we investigate conditions on a local ring R that imply every n × n upper triangular matrix ring over R is quasipolar. It is shown that this is the case for commutative local rings, as well as for a host of other classes of local
Jianlong Chen
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Functional identities in upper triangular matrix rings

Linear Algebra and its Applications, 2016
Let \(R\) be a subring of an associative ring \(Q\); one requires that \(R\) and \(Q\) share the same unit element. Denote \(\overline x_m=(x_1,\ldots,x_m)\in R^m\) and let \(\overline x_m^i\) be the ``vector'' \(\overline x_m\) without its \(i\)-th coordinate, analogously \(\overline x_m^{ij}\) stands for the same vector picking out its coordinates ...
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