Abstract
W. D. Munn and R. Penrose (1957) obtained an explicit formula for the identity element 1A of the semigroup algebra A of an arbitrary finite inverse semigroup S. An alternative (inductive) characterization of 1A is presented, giving new information about how the form of 1A depends on the Vagner-Preston order in S.
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References
G. Lallement, Semigroups and Combinatorial Applications, Wiley, New York, 1979
W. D. Munn, ‘Matrix representations of semigroups’, Proc. Cambridge Phil. Soc. 53 (1957), 5–12.
G.-C. Rota, ‘On the foundations of combinatorial theory I. Theory of Möbius functions’, Zeit. Wahrscheinlichkeit 2 (1964), 340–368.
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© 1987 D. Reidel Publishing Company
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Drazin, M.P. (1987). The Identity Element in Inverse Semigroup Algebras. In: Goberstein, S.M., Higgins, P.M. (eds) Semigroups and Their Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3839-7_5
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DOI: https://doi.org/10.1007/978-94-009-3839-7_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8209-9
Online ISBN: 978-94-009-3839-7
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