The Algebra of Strongly Full Terms
نویسندگان
چکیده
The well-known connection between hyperidentities of an algebra and identities satisfied by the clone of this algebra is studied here in a restricted setting, that of n-ary strongly full hyperidentities and identities of the n-ary clone of term operations of an algebra induced by strongly full terms, both of a type consisting only of n-ary operation symbols. We call such a type an n-ary type. Using the concept of a weakly invariant congruence relation we characterize varieties of n-ary type whose identities consist of strongly full terms which are closed under taking of isomorphic copies of their clones of all strongly full n-ary term operations. Finally, we show that a variety of n-ary type defined by identities consisting of strongly full terms has this property if and only if it is OSF -solid for the monoid OSF of all strongly full hypersubstitutions which have surjective extensions. AMS Mathematics Subject Classification (2000): 08A40, 08A60, 08A02
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