Abstract
Abstract: For a monoid M , we introduce strongly semicommutative rings relative to M , which are a generalization of strongly semicommutative rings, and investigates its properties. We show that every reduced ring is strongly M -semicommutative for any unique product monoid M. Also it is shown that for a monoid M and an ideal I of R. If I is a reduced ring and R/I is strongly M -semicommutative, then R is strongly M -semicommutative.
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