Regularity of monoids under Schutzenberger products

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In this paper we give a partial answer to the problem which is about the regularity of Schutzenberger products in semigroups asked by Gallagher in his thesis [Problem 6.1.6]{Gallagher} and, also, we investigate the regularity for the new version of the Schutzenberger product which was defined in [Ates].
8 pages

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