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Automorphism groups of sandwich semigroups

  • K. D. Magill (a1)

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Sandwich semigroups were introduced in [4], [5] and [6]. Green's relations (for regular elements) were characterized for these semigroups in [11] and [13]. Sandwich semigroups of continuous functions first made their appearance in [5]. In this paper, we consider only sandwich semigroups of continuous functions and we refer to them simply as sandwich semigroups. We now recall the definition. Let X and Y be topological spaces and fix a continuous function α from Y into X. Let S(X, Y, α) denote the semigroup of all continuous functions from X into Y where the product fg of f, g ε S(X, Y, α) is defined by fg = f ∘ α ∘ g. We refer to S(X, Y, α) as a sandwich semigroup with sandwich function α. If X = Y and α is the identity map then S(X, Y, α) is, of course, just S(X), the semigroup of all continuous selfmaps of X.

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2.Hickey, J. B.. Semigroups under a sandwich operation. Proc. Edinburgh Math. Soc., 26 (1983), 371382.
3.Hickey, J. B.. On variants of a semigroup. Bull. Austral. Math. Soc., 34 (1986), 447459.
4.Magill, K. D. Jr. Semigroup structures for families of functions, I; some homorphism theorems. J. Austral. Math. Soc., 7 (1967), 8194.
5.Magill, K. D. Jr. Semigroup structures for families of functions, II; continuous functions. J. Austral. Math. Soc., 7 (1967), 95107.
6.Magill, K. D. Jr. Semigroup structures for families of functions, III; R*t semigroups. J. Austral. Math. Soc., 7 (1967), 524538.
7.Magill, K. D. Jr. Green's I-relation for polynomials. Semigroup Forum, 16 (1978), 165182.
8.Magill, K. D. Jr. Automorphism groups of laminated near-rings. Proc Edinburgh Math. Soc., 23 (1980), 97102.
9.Magill, K. D. Jr. Isomorphisms of sandwich near-rings of continuous functions. Bollettino U.M.I., 6 (1986), 209222.
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