scholarly journals Functional identities on upper triangular matrix rings

2020 ◽  
Vol 18 (1) ◽  
pp. 182-193
Author(s):  
He Yuan ◽  
Liangyun Chen
Keyword(s):  
Triangular Matrix ◽  
Matrix Rings ◽  
Unital Ring ◽  
Functional Identities ◽  
Upper Triangular Matrix ◽  
Free Subset

Abstract Let R be a subset of a unital ring Q such that 0 ∈ R. Let us fix an element t ∈ Q. If R is a (t; d)-free subset of Q, then Tn(R) is a (t′; d)-free subset of Tn(Q), where t′ ∈ Tn(Q), $\begin{array}{} t_{ll}' \end{array} $ = t, l = 1, 2, …, n, for any n ∈ N.

scholarly journals On p.p.-rings which are reduced

2006 ◽  
Vol 2006 ◽  
pp. 1-5
Author(s):  
Xiaojiang Guo ◽  
K. P. Shum
Keyword(s):  
Triangular Matrix ◽  
Matrix Rings ◽  
Upper Triangular Matrix

Denote the2×2upper triangular matrix rings overℤandℤpbyUTM2(ℤ)andUTM2(ℤp), respectively. We prove that if a ringRis a p.p.-ring, thenRis reduced if and only ifRdoes not contain any subrings isomorphic toUTM2(ℤ)orUTM2(ℤp). Other conditions for a p.p.-ring to be reduced are also given. Our results strengthen and extend the results of Fraser and Nicholson on r.p.p.-rings.

scholarly journals Derivations of upper triangular matrix rings

1993 ◽  
Vol 187 ◽  
pp. 263-267 ◽  
Author(s):  
Sǒnia P. Coelho ◽  
C. Polcino Milies
Keyword(s):  
Triangular Matrix ◽  
Matrix Rings ◽  
Upper Triangular Matrix

Integer-valued polynomials over block matrix algebras

2019 ◽  
Vol 19 (03) ◽  
pp. 2050053
Author(s):  
J. Sedighi Hafshejani ◽  
A. R. Naghipour ◽  
M. R. Rismanchian
Keyword(s):  
Matrix Ring ◽  
Triangular Matrix ◽  
Block Matrix ◽  
Quotient Field ◽  
Matrix Rings ◽  
Matrix Algebras ◽  
Triangular Matrix Ring ◽  
Upper Triangular Matrix ◽  
Full Matrix Ring ◽  
Upper Triangular Matrix Ring

In this paper, we state a generalization of the ring of integer-valued polynomials over upper triangular matrix rings. The set of integer-valued polynomials over some block matrix rings is studied. In fact, we consider the set of integer-valued polynomials [Formula: see text] for each [Formula: see text], where [Formula: see text] is an integral domain with quotient field [Formula: see text] and [Formula: see text] is a block matrix ring between upper triangular matrix ring [Formula: see text] and full matrix ring [Formula: see text]. In fact, we have [Formula: see text]. It is known that the sets of integer-valued polynomials [Formula: see text] and [Formula: see text] are rings. We state some relations between the rings [Formula: see text] and the partitions of [Formula: see text]. Then, we show that the set [Formula: see text] is a ring for each [Formula: see text]. Further, it is proved that if the ring [Formula: see text] is not Noetherian then the ring [Formula: see text] is not Noetherian, too. Finally, some properties and relations are stated between the rings [Formula: see text], [Formula: see text] and [Formula: see text].

Zero Divisor Graphs of Upper Triangular Matrix Rings

2013 ◽  
Vol 41 (12) ◽  
pp. 4622-4636 ◽  
Author(s):  
Aihua Li ◽  
Ralph P. Tucci
Keyword(s):  
Zero Divisor ◽  
Triangular Matrix ◽  
Matrix Rings ◽  
Upper Triangular Matrix
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