$\cal J$-classes in the direct product of two semigroups
Imrich Fabrici · Czechoslovak Mathematical Journal · 1994
In [3] the mutual relation between a principal two-sided ideal J (a, 6) in the direct product of two semigroups and the direct product of two principal two-sided ideals J(a) x J(b) is investigated.In particular, some conditions are given under which J(a,b) = J(a) x J(b) holds.The aim of the present paper is to study the mutual relation between a J?-class J( a ,6) in 5i x 5 2 and the direct product J a x J b of two ^-classes both in the general case and in the special case of maximal ^-classes.Finally, we give conditions under which J(*j>) ~ Ja x Jb.All notions and notations which are not defined are meant as in [1].