An Expanded Concept and Graph of Zadeh’s Algebraic Operations for 3‐Dimensional Generalized Triangular Fuzzy Sets [PDF]
, 2022 Yong Sik Yun
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Jordan maps on triangular algebras
Linear Algebra and its Applications, 2007 For \(x,y\in R\), an associative ring, let \(x\circ y=xy+yx\). Given rings \(R\) and \(S\), maps \(f\colon R\to S\) and \(g\colon S\to R\) form a Jordan pair if for all \(x\in R\) and \(y\in S\), \(f(x\circ g(y))=f(x)\circ y\) and \(g(y\circ f(x))=g(y)\circ x\).
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Lie triple derivation of the Lie algebra of strictly upper triangular matrix over a commutative ring
, 2009 Let N ( n , R ) be the nilpotent Lie algebra consisting of all strictly upper triangular n × n matrices over a 2-torsionfree commutative ring R with identity 1.
Hengtai Wang, Qingguo Li
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On Derivations of Certain Algebras Related to Irreducible Triangular Algebras [PDF]
Transactions of the American Mathematical Society, 1983 This paper deals with derivations on algebras that are generated by a maximal abelian selfadjoint algebra of operators A \mathcal {A}
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$\\mathbb{Z}_2$-graded polynomial identities for the Jordan algebra of\n $2\\times 2$ upper triangular matrices [PDF]
, 2020 Dimas José Gonçalves +1 more
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Automorphisms of the Lie algebra of strictly upper triangular matrices over a commutative ring
, 2001 Let R be an arbitrary commutative ring with identity. Denote by n(R) the Lie algebra over R consisting of all strictly upper triangular (n+1)×(n+1) matrices over R with n⩾3. In addition, for n=3 assume that the annihilator of 2 in R is zero.
You'an Cao, Zuowen Tan
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Representation dimensions of triangular matrix algebras
Linear Algebra and its Applications, 2013 19 ...
Yin, Hongbo, Zhang, Shunhua
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A note on algebra automorphisms of strictly upper triangular matrices over commutative rings
, 2000 In this note, we explicitly describe the automorphism group of the R-algebra of strictly upper triangular n×n matrices over an arbitrary commutative ring.
You'an Cao, Jingtong Wang
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Complexity of triangular representations of algebraic sets
Journal of Algebra, 2019 Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Szanto. In this paper, we give the first complete bounds for the degrees of the polynomials and the number of components in the output of the algorithm, providing explicit ...
Eli Amzallag +3 more
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Involutions for upper triangular matrix algebras
Advances in Applied Mathematics, 2006 The first result in the paper under review is the description of the involutions of the first kind (which fix the centre) of the algebra \(UT_n(F)\) of \(n\times n\) upper triangular matrices over a field of characteristic different from 2. The authors show that, up to isomorphism of algebras with involution, there are two types of involutions.
Onofrio Mario Di Vincenzo +2 more
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