Results 11 to 20 of about 2,891 (214)

Jordan isomorphisms of upper triangular matrix rings

Linear Algebra and its Applications, 2007
A bijective additive map of rings \(g\colon A\to B\) is a Jordan isomorphism if for all \(x,y\in A\), \(g(xy+yx)=g(x)g(y)+g(y)g(x)\). The authors generalize results in the literature that show when such a map is a ring isomorphism or anti-isomorphism. They consider a Jordan isomorphism \(g\colon S\to B\) for \(S\) the ring of upper triangular \(n\times
Liu, Cheng-Kai, Tsai, Wan-Yu
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Jordan homomorphisms of upper triangular matrix rings

Linear Algebra and its Applications, 2013
Let \(T_n(R)\) denote the ring of all upper triangular matrices over a ring \(R\). The main result of the paper states that a Jordan homomorphism \(\varphi\) from \(T_n(R)\) onto \(T_{n'}(R)\), where \(n,n'\geq 2\), is either a homomorphism or an antihomomorphism provided that \(R\) is a unital ring without nontrivial idempotents and \(\varphi(R\cdot 1)
Wang, Yao, Wang, Yu
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Derivations of upper triangular matrix rings

Linear Algebra and its Applications, 1993
Let \(R\) be a ring with unity. The authors consider derivations of the ring \(T_ n(R)\), the ring of \(n\times n\) upper triangular matrices over \(R\). For a derivation \(d\) of \(R\), \(\overline{d}\) denotes the derivation that is induced by \(d\) on \(T_ n(R)\).
Coelho, Sǒnia P., Polcino Milies, C.
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GENERALIZED CAYLEY GRAPH OF UPPER TRIANGULAR MATRIX RINGS

Bulletin of the Korean Mathematical Society, 2016
Summary: Let \(R\) be a commutative ring with the non-zero identity and \(n\) be a natural number. \(\Gamma ^n_R\) is a simple graph with \(R^n\setminus\{0\}\) as the vertex set and two distinct vertices \(X\) and \(Y\) in \(R^{n}\) are adjacent if and only if there exists an \(n \times n\) lower triangular matrix \(A\) over \(R\) whose entries on the ...
Afkhami, Mojgan, Hashemifar, Seyed Hosein, Khashyarmanesh, Kazem   +2 more
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A SUBCLASS OF BAER IDEALS AND ITS APPLICATIONS [PDF]

Journal of Algebraic Systems
An ideal $I$ of a ring $R$ is called a right strongly Baer ideal if $r(I)=r(e)$, where $e$ is an idempotent, and there are right semicentral idempotents $e_{i}$ ($1\leq i\leq n$) with $ReR=Re_{1}R\cap Re_{2}R\cap...\cap Re_{n}R$ and each ideal $Re_{i}R ...
Zainab Gharabagi, Ali Taherifar
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On p.p.-rings which are reduced

International Journal of Mathematics and Mathematical Sciences, 2006
Denote the 2×2 upper triangular matrix rings over ℤ and ℤp by UTM2(ℤ) and UTM2(ℤp), respectively. We prove that if a ring R is a p.p.-ring, then R is reduced if and only if R does not contain any subrings isomorphic to UTM2(ℤ) or UTM2(ℤp).
Xiaojiang Guo, K. P. Shum
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Decomposition of Automorphisms of Certain Solvable Subalgebra of Symplectic Lie Algebra over Commutative Rings

International Journal of Mathematics and Mathematical Sciences, 2012
Let Cl+1(R) be the 2(l+1)×2(l+1) matrix symplectic Lie algebra over a commutative ring R with 2 invertible. Then tl+1CR  =  {m-1m-20-m-1T ∣ m̅1 is an l+1 upper triangular matrix, m̅2T=m̅2,  over  R} is the solvable subalgebra of Cl+1(R).
Xing Tao Wang, Lei Zhang
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A STUDY ON TRI REVERSIBLE RINGS [PDF]

Journal of Algebraic Systems
This article embodies a ring theoretic property which, preserves the reversibility of elements at non-zero tripotents. A ring R is defined as quasi tri reversible if any non-zero tripotent element ab of R implies ba is also a tripotent element in R for a,
Hussain Mohammed Imdadul Hoque, Helen Saikia   +1 more
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Some extensions of right N-semilocal rings

Journal of Scientific Research in Science
In this paper, we study the necessary and sufficient conditions for the formal triangular matrix ring, the generalized upper triangular matrix ring, the trivial Morita context, and the Morita context to be right N-semilocal, right N-semiperfect, right N ...
Samah H. El-Bishlawy, Abdelrahman M. Hassanein, Samia M. Abdelwahab   +2 more
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On biderivations of upper triangular matrix rings

Linear Algebra and its Applications, 2013
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