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2001, br. 5, str. 7-18
Primitive idempotents in semi-groups
(naslov ne postoji na srpskom)
aUniverzitet u Nišu, Ekonomski fakultet
bUniverzitet u Nišu, Prirodno-matematički fakultet, Odsek informatika

e-adresasbogdan@pmf.pmf.ni.ac.yu, ciricm@bankerinter.net
Ključne reči: idempotents; primitive idempotents; semi-groups; E-inversive semi-groups; B-inversive semigroups; ideals; minimal ideals
Sažetak
(ne postoji na srpskom)
In this paper we study certain general properties of primitive and 0-primitive idempotents, and the obtained results we apply to 0-inversive E-inversive and B-inversive semi-groups. We also determine some conditions under which a left ideal of a semi-group with zero generated by a nonzero idempotent is left 0-simple. The obtained results generalize some results by Venkatesan, Steinfeld, Bogdanović and Milić, Bogdanović and Ćirić, Mitsch and Petrich and others.
Reference
Bogdanović, S. (1985) Semi-groups with a system of semi-groups. Novi Sad: Inst. of Math
Bogdanović, S., Ćirić, M. (1992) Primitive π-regular semi-groups. Proc. Japan Academy, Ser. A 68, 344-337
Bogdanović, S., Ćirić, M. (1993) Semi-groups. Niš: Prosveta
Bogdanović, S., Gilezan, S. (1982) Demigroups with completely simple kernel. Zbornik Radova PMF, Novi Sad, 12, 429-445
Bogdanović, S.M., Milić, S. (1984) A nil-extension of a completely simple semi-group. Publications de l'Institut mathematique, 36 (50), 45-50
Catino, F., Miccoli, M.M. (1989) On semidirect products of semi-groups. Note di Matematica, 9 (2), 189-194
Clifford, A.H., Preston, G.B. (1961) The algebraic theory of semigroups. Providence, RI: American Mathematical Society / AMS, vol. 1
Clifford, A.H., Preston, G.B. (1967) The algebraic theory of semigroups. Providence, RI: American Mathematical Society / AMS, vol. 2
Fountain, J. (1982) Abundant semi-groups. Proc. London Math. Soc, 44 (3), 103-129
Hall, T. (1970) On the natural order of I-class and of idempotents in a regular semi-group. Glasgow Math. J, 11, 167-168
Higgins, P.M. (1997) The converse of Lallement's lemma. u: Howie J.M., Ruskuc N. [ur.] Proceedings of the Conference 'Semi-groups and Applications', St. Andrews, World Scientific, 78-86
Howie, J.M. (1995) Fundamentals of semigroup theory. u: London Math. Soc. Monographs, New Series, Oxford: Clarendon Press
Lallement, G. (1964) Sur les homomorphismes d'un demi-groups an demo-groups complètement 0-simple. C.R. Acad. Sci., Paris, 258, 3609-3612
Lallement, G., Petrich, M. (1966) Décompositions I-matricielles d'un demi-groupe. J. Math. Pores Appl, 45, 67-117
Mitsch, H. (1997) On E- and 0-inversive semi-groups. u: Abstracts of Lectures, Semigroups and Applications, St. Andrews
Preston, G.B. (1969) Matrix representations of inverse semi-groups. J. Austral. Math. Soc, 9, 29-61
Steinfeld, O. (1966) On semi-groups which are unions of completely 0-simple semi-groups. Czech. Math. J, 16, 63-69
Steinfeld, O. (1978) Quasi-ideals in rings and semi-groups. Budapest: Adadmiai Kiado
Thierrin, G. (1952) Sur les demi-groupes inversés. C.R. Acad. Sci., Paris, 234, 1336-1338
Venkatesan, P.S. (1962) On a class inverse groups. Amer. J. Math, 84, 578-582
Venkatesan, P.S. (1966) On decomposition of semi-groups with zero. Math. Zeitsch, 92, 164- 174
 

O članku

jezik rada: engleski
vrsta rada: članak
DOI: 10.5937/MatMor0105007B
objavljen u SCIndeksu: 05.05.2008.

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