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On bi-\(\Gamma\)-ideals in \(\Gamma\)-semigroups with involution. (English) Zbl 1432.20044

Summary: The concept of involution in semigroups was given by T. E. Nordahl and H. E. Scheiblich [Semigroup Forum 16, 369–377 (1978; Zbl 0408.20043)]. In this paper, we introduce involution in \(\Gamma\)-semigroups. Also, we define bi-\(\Gamma\)-ideals in \(\Gamma\)-semigroups with involution and prove many interesting results characterizing \(\Gamma\)-semigroups with involution by using bi-\(\Gamma\)-ideals.

MSC:

20M75 Generalizations of semigroups
20M12 Ideal theory for semigroups

Citations:

Zbl 0408.20043
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