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Title: One-sided principal ideals in the direct product of two semigroups (English)
Author: Fabrici, Imrich
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 118
Issue: 4
Year: 1993
Pages: 337-342
Summary lang: English
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Category: math
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Summary: A necessary and sufficient condition is given for a) a principal left ideal $L(s,t)$ in $S\times T$ to be equal to the direct product of the corresponding principal left ideals $L(s)\times L(t)$, b) an $\Cal L$-class $L_{(s,t)}$ to be equal to the direct product of the corresponding $\Cal L$-classes $L_s\times L_t$. (English)
Keyword: principal left ideal
Keyword: direct product
Keyword: direct product of two semigroups
MSC: 20M10
MSC: 20M12
MSC: 20M15
idZBL: Zbl 0810.20043
idMR: MR1251880
DOI: 10.21136/MB.1993.126156
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Date available: 2009-09-24T21:01:02Z
Last updated: 2020-07-29
Stable URL: http://hdl.handle.net/10338.dmlcz/126156
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Reference: [1] Abrhám I.: On (H, T)-ideals in the direct product of semigroups.Mat. časopis 21 (1971), 199-211.
Reference: [2] Clifford A.H., Preston G.B.: The algebraic theory of semigroups.American Math. Soc., Providence, R.I., 1961. Zbl 0111.03403, MR 0132791
Reference: [3] Fabrici I.: On semiprime ideals in the direct product of semigroups.Mat. časopis 18 (1968), 201-203. MR 0237674
Reference: [4] Ivan J.: On the direct product of semigroups.Mat.-fyz. časopis (1953), 57-66. MR 0062733
Reference: [5] Petrich M.: Prime ideals in the cartesian product of two semigroups.Czechoslov. Math. J. 12 (1962), 150-152. MR 0140597
Reference: [6] Petrich M.: Introduction to semigroups.Charles E. Merrill Publishing CO. A Bell and Howell Company, Ohio. Zbl 0321.20037, MR 0393206
Reference: [7] Plemmons R.: Maximal ideals in the direct product of two semigroups.Czechoslov. Math. J. 17 (1967), 257-260. Zbl 0189.02001, MR 0214681
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