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Miklos Schweitzer 1975_3

Source: semigroup without proper two-sided ideals

December 30, 2008
superior algebrasuperior algebra unsolved

Problem Statement

Let S S be a semigroup without proper two-sided ideals and suppose that for every a,b∈S a,b \in S at least one of the products ab ab and ba ba is equal to one of the elements a,b a,b. Prove that either ab\equal{}a for all a,b∈S a,b \in S or ab\equal{}b for all a,b∈S a,b \in S. L. Megyesi
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