Non-Associative Rings of Infinite Matrices

AbstractIn the classical theory of plane deformations in isotropic plastic media, the field equations are hyperbolic and the orthogonal families of characteristics are known as Hencky-Prandtl nets. Their distinctive geometry has been given symbolic expression by Collins (1968), in an algebra of infinite matrices associated with canonical series representations of the general solution. This has become the standard technique when investigating boundary-value problems, both analytically and numerically. The basic framework of the algebra is here reorganized and developed. A systematic approach then leads to new identities which are shown to be fundamental in the algebraic hierarchy.

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Fine Spectra of Tridiagonal Symmetric Matrices

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2011/161209 ◽

2011 ◽

Vol 2011 ◽

pp. 1-10 ◽

Cited By ~ 4

Author(s):

Muhammed Altun

Keyword(s):

Explicit Form ◽

Resolvent Operator ◽

Sequence Spaces ◽

Symmetric Matrices ◽

Infinite Matrices ◽

Banded Matrices ◽

Lower Triangular ◽

The Resolvent Operator

The fine spectra of upper and lower triangular banded matrices were examined by several authors. Here we determine the fine spectra of tridiagonal symmetric infinite matrices and also give the explicit form of the resolvent operator for the sequence spaces , , , and .

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Varieties satisfying semigroup identities: Algebras over a finite field and rings

International Journal of Algebra and Computation ◽

10.1142/s0218196716500417 ◽

2016 ◽

Vol 26 (05) ◽

pp. 985-1017

Author(s):

Olga B. Finogenova

Keyword(s):

Finite Field ◽

Associative Algebras ◽

Adjoint Semigroup ◽

Semigroup Identities ◽

Associative Rings

We study varieties of associative algebras over a finite field and varieties of associative rings satisfying semigroup or adjoint semigroup identities. We characterize these varieties in terms of “forbidden algebras” and discuss some corollaries of the characterizations.

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Representation of doubly infinite matrices as non-commutative Laurent series

Special Matrices ◽

10.1515/spma-2017-0018 ◽

2017 ◽

Vol 5 (1) ◽

pp. 250-257 ◽

Cited By ~ 2

Author(s):

María Ivonne Arenas-Herrera ◽

Luis Verde-Star

Keyword(s):

Laurent Series ◽

Infinite Matrices ◽

General Properties ◽

Hessenberg Matrices ◽

Diagonal Representation

Abstract We present a new way to deal with doubly infinite lower Hessenberg matrices based on the representation of the matrices as the sum of their diagonal submatrices. We show that such representation is a simple and useful tool for computation purposes and also to obtain general properties of the matrices related with inversion, similarity, commutativity, and Pincherle derivatives. The diagonal representation allows us to consider the ring of doubly infinite lower Hessenberg matrices over a ring R as a ring of Laurent series in one indeterminate, with coefficients in the ring of R-valued sequences that don’t commute with the indeterminate.

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