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- W2033809543 abstract "If R is a ring graded by the semigroup S , then the smash product ring R # S ∗ can be constructed, and in many situations retains categorical “realization” properties analogous to those of the group-graded case. In particular, if S acts as endomorphisms on the ring A , then skew semigroup rings of the form A ∗ S ∗ and S ∗ ∗ A are graded by S , so we may form the “skew-smash” rings (A ∗ S ∗ ) # S ∗ and (S ∗ ∗ A) # S ∗ . On the other hand, S acts as endomorphisms on any ring of the form R # S ∗ , so that the skew semigroup rings (R # S ∗ ) ∗ S ∗ and S ∗ ∗ (R # S ∗ ) may be produced. In particular we may perform this construction when R itself is a skew semigroup ring of the form A ∗ S ∗ or S ∗ ∗ A , thereby yielding “skew-smash-skew” rings. In this article we analyze the resulting skew-smash and skew-smash-skew rings, and prove that each can be realized as a skew semigroup ring for an appropriate ring and (possibly new) semigroup. Inherent in our investigation is the description of a number of methods by which given semigroups can be used to produce new, related semigroups. As one consequence of our results we provide a broader context for some of the group-theoretic “duality” results of Cohen and Montgomery." @default.
- W2033809543 created "2016-06-24" @default.
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- W2033809543 date "1996-05-01" @default.
- W2033809543 modified "2023-09-24" @default.
- W2033809543 title "Duality theorems for finite semigroups" @default.
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- W2033809543 doi "https://doi.org/10.1016/0022-4049(96)00082-5" @default.
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