부산대학교 도서관

In this paper we consider mappings which map the binary operation symbol f to the term σ(f) which do not necessarily preserve the arities. We call these mappings generalized hypersubstitutions. Any generalized hypersubstitution σ can be extended to a mapping σ on the set of all terms of type τ ＝ (2). We define a binary operation on the set Hyp_G(2) of all generalized hypersubstitutions of type τ ＝ (2) by using this extension. The set Hyp_G(2) together with the identity generalized hypersubstitution σ_(id) which maps f to the term f(x₁, x₂) forms a monoid. We determine all regular elements of this monoid.