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Orthodox bands of modules

Published online by Cambridge University Press:  17 April 2009

F. Pastijn
Affiliation:
Dienst Hogere Meetkunde, Rijksuniversiteit Gent, Krijgslaan. Gent, Belgium.
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Abstract

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In this paper we shall consider orthodox bands of commutative groups, together with a ring of endomorphisms. We shall generalize the concept of a left module by introducing orthodox bands of left modules; we shall also deal with linear mappings, the transpose of a linear mapping and with the dual of an orthodox band of left modules.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Bourbaki, N., Éléments de mathématique, Fascicule VI. Première partie, Livre II, Algèbre; Chapter 2, Algèbre linéaire, 3e édition (Hermann, Paris, 1967).Google Scholar
[2]Clifford, A.H., “The structure of orthodox unions of groups”, Semigroup Forum 3 (1971/1972), 283337.CrossRefGoogle Scholar
[3]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups, Volume I (Mathematical Surveys, 7. Amer. Math. Soc., Providence, Rhode Island, 1961).Google Scholar
[4]Firsov, *J.M., “Everywhere defined semimodules” (Russian), Summaries of talks of the all-union algebraic symposium, 360361 (Gomel, 1975).Google Scholar
[5]Hewitt, E. and Zuckerman, H.S., “Finite dimensional convolution algebras”, Acta Math. 93 (1955), 67119.CrossRefGoogle Scholar
[6]Pastijn, F. and Reynaerts, H., “Semilattices of modules”, submitted.Google Scholar
[7]Schwarz, *Štefan, “The theory of characters of finite commutative semigroups” (Russian), Czechoslovak Math. J. 4 (79)(1954), 219247.CrossRefGoogle Scholar
[8]Warne, R.J. and Williams, L.K., “Characters on inverse semigroups”, Czechoslovak Math. J. 11 (86)(1961), 150155.CrossRefGoogle Scholar
[9]Wuytack, F. and Depunt, J., “Operators over I-collections of modules”, Bull. Soc. Math. Belg. 17 (1965), 3754.Google Scholar
[10]Yamada, Miyuki, “Strictly inversive semigroups”, Bull. Shimane Univ. Natur. Sci. 13 (1963), 128138.Google Scholar
[11]Yamada, Miyuki and Kimura, Naoki, “Note on idempotent semigroups II”, Proc. Japan Acad. 34 (1958), 110112.Google Scholar