Morita Equivalent Semigroups of Quotients
John K. Luedeman · Proceedings of the American Mathematical Society · 1980
Let S be a monoid and $_SM$ and $_SN$ be retracts of each other. We show that ${\text {End}_S}(M)$ and ${\text {End}_S}(N)$ are Morita equivalent. Using this result, we show that if A and B are Morita equivalent monoids, then their semigroups of quotients are Morita equivalent.