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- W2914027503 abstract "For a finite dimensional algebra A over an infinite field K, the subspace semigroup S(A) consists of all subspaces of A with operation V ∗ W = linK(VW). We describe the structure of S(A), showing in particular that, similarly to any algebraic linear semigroup, S(A) is strongly π-regular; we describe its regular elements and regular T-classes. As the key intermediate step, for an arbitrary connected algebraic monoid M, we study the semigroup C(M) consisting of all irreducible closed subsets with operation X · Y = XY, and we transfer the information to S(A) via the natural onto homomorphism C(A) → S(A). With potential applications in mind, our primary focus in this paper is on the case of the full matrix algebra A = Mn(K)." @default.
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- W2914027503 date "2000-11-01" @default.
- W2914027503 modified "2023-09-30" @default.
- W2914027503 title "Subspace Semigroups" @default.
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- W2914027503 doi "https://doi.org/10.1006/jabr.2000.8417" @default.
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