6533b828fe1ef96bd1288e93
RESEARCH PRODUCT
On the Directly and Subdirectly Irreducible Many-Sorted Algebras
J. Climent VidalJ. Soliveres Tursubject
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)description
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-03-01 | Demonstratio Mathematica |