^{1}Department of Mathematics and Computer Science, Prince of Songkla University, Pattani 94000, Thailand ^{2}Institute of Mathematics, University of Potsdam, Am Neuen Palais, Potsdam 14415, Germany

Received 8 January 2006; Revised 14 August 2006; Accepted 21 August 2006

A partial algebra 𝒜=(A;(fiA)i∈I)
consists of a set A and an indexed set (fiA)i∈I of partial operations
fiA:Ani⊸→A.
Partial operations occur in the algebraic description of partial recursive functions and Turing machines. A pair of terms
p≈q over the partial algebra 𝒜 is said to be a strong identity in 𝒜 if the right-hand side is defined whenever the left-hand side is defined and vice versa,
and both are equal. A strong identity p≈q is called a strong hyperidentity if when the operation symbols occurring in p and q are replaced by terms
of the same arity, the identity which arises is satisfied as a strong identity. If every strong identity in a strong variety of partial algebras is satisfied as a strong hyperidentity, the strong variety is called solid. In this paper, we consider the other extreme, the case when the set of all strong identities
of a strong variety of partial algebras is invariant only under the identical replacement of operation symbols by terms. This leads to the concepts of unsolid and fluid varieties and some generalizations.