JOURNAL ARTICLE
Semiprimitivity of inverse semigroup algebras
Year: 1982 Journal: Proceedings of the Royal Society of Edinburgh Section A Mathematics Vol: 93 (1-2)Pages: 83-98 Publisher: Cambridge University Press
Abstract
Synopsis Let S be an inverse semigroup and F a field. It is shown that if F has characteristic 0 and is not algebraic over its prime subfield then the algebra of S over F is semiprimitive (i.e. Jacobson semisimple). This generalises a well-known theorem on group algebras due to Amitsur. Similar results for the case in which F has prime characteristic are obtained under the additional hypotheses that S is completely semisimple or that S is E -unitary with a totally ordered semilattice.
Keywords:
Mathematics Semilattice Inverse semigroup Prime (order theory) Unitary state Semigroup Inverse Pure mathematics Field (mathematics) Algebra over a field Bicyclic semigroup Discrete mathematics Combinatorics
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15
Cited By
1.08
FWCI (Field Weighted Citation Impact)
22
Refs
0.74
Citation Normalized Percentile
Is in top 1%
Is in top 10%
Citation History
Topics
semigroups and automata theory
Physical Sciences → Computer Science → Computational Theory and Mathematics
Advanced Algebra and Logic
Physical Sciences → Computer Science → Computational Theory and Mathematics
Geometric and Algebraic Topology
Physical Sciences → Mathematics → Geometry and Topology
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