On the problems of equality and divisibility of words in a semigroup with a defining relation of the from

This paper studies the problem of left divisibility in a semigroup given by a single defining relation of the form $a=bA$, where $A$ is an arbitrary word in the alphabet $a,b$. Solvability of the problems of equality and left divisibility of words is proved for a semigroup given by a defining relation of the form $a=(bA)^na$, where $n>1$ .
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