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Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.

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Semi group of polynomials which all roots lie on the unit circle

This means that the semigroup of your polynomials is freely generated by the set of point on the unit circle, aka by $\{z-k | k:\mathbb C, |k|=1\}$. … It can be given a nicer structure if you consider the natural topology on the set of polynomials. In this case it will be the free topological abelian group generated by the unit circle $S^1$. …
Anton Fetisov's user avatar