Results 191 to 200 of about 2,891 (214)

Integer-valued polynomials on subsets of upper triangular matrix rings

Communications in Algebra
A R Naghipour, J Sedighi Hafshejani
exaly   +2 more sources

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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Model theory of strictly upper triangular matrix rings

Journal of Symbolic Logic, 1980
Two questions on rings of strictly upper triangular matrices arising from B. Rose's work [5] are answered in this paper. An n × n matrix (αi, j) is strictly upper triangular if αi, j = 0 whenever i ≥ j. The ring of strictly upper triangular n × n matrices with entries from a field F will be denoted by Sn(F).
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Functional identities in upper triangular matrix rings revisited

Linear and Multilinear Algebra, 2017
The aim of this paper is to give an improvement of a result on functional identities in upper triangular matrix rings obtained by Eremita, which presents a short proof of Eremita’s result.
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The ℵ₁-categoricity of strictly upper triangular matrix rings over algebraically closed fields

Journal of Symbolic Logic, 1978
AbstractLet n ≥ 3. The following theorems are proved.Theorem. The theory of the class of strictly upper triangular n × n matrix rings over fields is finitely axiomatizable.Theorem. If R is a strictly upper triangular n × n matrix ring over a field K, then there is a recursive map σ from sentences in the language of rings with constants for K into ...
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Semicentral idempotents of upper triangular matrix rings

Journal of Algebra and Its Applications
In this paper, we describe the necessary and sufficient conditions for upper triangular [Formula: see text] matrix over a ring to be left (right) semicentral idempotent. Circle compositions of left and right semicentral idempotent matrices ([Formula: see text]) are considered. Many researchers deal with the problems of expressing various matrices as a
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On the Cayley graphs of upper triangular matrix rings

2018
The authors define a Cayley digraph on upper triangular matrices over a ring, and prove a number of properties about this very specific family of digraphs (diameter, planarity, girth, etc.). No real motivation is provided for the particular connection set or the vertex set they choose.
Moosavi, Nazila Vaez, Khashyarmanesh, Kazem, Mohammadikhah, Sadegh, Afkhami, Mojgan   +3 more
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K i of Upper Triangular Matrix Rings

Proceedings of the American Mathematical Society, 1976
R. Keith Dennis, Susan C. Geller
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The Injective Envelope of the Upper Triangular Matrix Ring

The American Mathematical Monthly, 1971
E. E. Bray, K. A. Byrd, R. L. Bernhardt
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Commutative local rings over which every upper-triangular matrix is the sum of an idempotent and a q-potent that commute

Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
We study commutative local rings over which every upper-triangular matrix is the sum of an idempotent and a $q$-potent that commute. For Galois rings and rings of the form $\mathbb{F}_{p^{k}}[x]/\langle x^{r} \rangle$, necessary and sufficient criterion are provided.
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