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