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Principal two-sided ideals in the direct product of two semigroups. (English) Zbl 0751.20043
It is completely described when the direct product of two principal ideals of the components in the direct product of two semigroups is itself a principal ideal.

##### MSC:
 20M12 Ideal theory for semigroups
##### Keywords:
direct product; principal ideals
Full Text:
##### References:
 [1] Clifford A. H., Preston G. B.: The algebraic theory of semigroups. American Math. Society, Providence, Vol. I) · Zbl 0111.03403 [2] Fabrici I.: One-sided principal ideals in the direct product of two semigroups. Math. Slovaca · Zbl 0810.20043 [3] Fabrici I.: On semiprime ideals of the direct product of semigroups. Math. časopis 18 (1968), 201-203. · Zbl 0172.02404 [4] Ivan J.: On the direct product of semigroups. Mat.-Fyz. časopis, 3 (1953), 57-66. [5] Petrich M.: Prime ideals in cartesian product of two semigroups. Czechoslov. Math. J., 12 (1962), 150-152. · Zbl 0124.25702 [6] Plemmons R.: Maximal ideals in the direct product of two semigroups. Czechoslov. Math. J. 17 (1967), 257-260. · Zbl 0189.02001
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