Search results for "Subdirectly irreducible algebra"

showing 3 items of 3 documents

Subdirectly irreducible generalized sums of upper semilattice ordered systems of algebras

2002

In [15] the generalized sum of an upper (F 1 , F 2 )-semilattice ordered system of algebras was defined. In this paper we find necessary and sufficient conditions under which this construction yields subdirectly irreducible algebras.

CombinatoricsAlgebra and Number TheorySubdirectly irreducible algebraMathematics::Rings and AlgebrasMathematics::General TopologySemilatticeAlgebra over a fieldMathematicsAlgebra Universalis
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q-Fock Space Representations of the q-Lorentz Algebra and Irreducible Tensors

1993

We present the q-deformation of the Lorentz algebra, with Hopf structure, in terms of four independent harmonic oscillators. The explicit realization of the q-Fock space is given and the irreducible finite-dimensional representations of so(1,3)q are described and characterized by its two q-Casimir operators. The concept of irreducible q-Lorentz tensor is also introduced. The analysis is made for a real deformation parameter.

Pure mathematics010308 nuclear & particles physicsLorentz transformation010102 general mathematics(gK)-moduleIrreducible elementSpace (mathematics)01 natural sciencesFock spaceAlgebrasymbols.namesakeSubdirectly irreducible algebra0103 physical sciencessymbolsTensor0101 mathematicsRealization (systems)Mathematics
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On the Directly and Subdirectly Irreducible Many-Sorted Algebras

2015

AbstractA theorem of single-sorted universal algebra asserts that every finite algebra can be represented as a product of a finite family of finite directly irreducible algebras. In this article, we show that the many-sorted counterpart of the above theorem is also true, but under the condition of requiring, in the definition of directly reducible many-sorted algebra, that the supports of the factors should be included in the support of the many-sorted algebra. Moreover, we show that the theorem of Birkhoff, according to which every single-sorted algebra is isomorphic to a subdirect product of subdirectly irreducible algebras, is also true in the field of many-sorted algebras.

Pure mathematicslcsh:MathematicsGeneral MathematicsSubalgebraUniversal enveloping algebralcsh:QA1-939directly irreducible many-sorted algebraSubdirect productsymbols.namesakemany-sorted algebraSubdirectly irreducible algebraAlgebra representationsymbolsDivision algebraMathematics::Metric GeometryCellular algebrasupport of a many-sorted algebrasubdirectly irreducible many-sorted algebraMathematicsFrobenius theorem (real division algebras)Demonstratio Mathematica
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