On the Group of Automorphisms of Universal Algebra and Many Sorted Algebra

نویسنده

  • Artur Korniłowicz
چکیده

The aim of the article is to check the compatibility of the automorphisms of universal algebras introduced in [10] and the corresponding concept for many sorted algebras introduced in [11]. In this paper U 1 is a universal algebra and f , g are functions from U 1 into U 1. We now state the proposition (1) id the carrier of U 1 is an isomorphism of U 1 and U 1. Let us consider U 1. The functor UAAut(U 1) yields a non empty set of functions from the carrier of U 1 to the carrier of U 1 and is defined by the conditions (Def. 1). (Def. 1)(i) Every element of UAAut(U 1) is a function from U 1 into U 1 , and (ii) for every function h from U 1 into U 1 holds h ∈ UAAut(U 1) iff h is an isomorphism of U 1 and U 1. Next we state several propositions: (2) UAAut(U 1) ⊆ (the carrier of U 1) the carrier of U 1. 1 The proposition (3) has been removed.

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تاریخ انتشار 1994