In this paper all subdirectly irreducible pseudocomplemented distributive lattices are found. This result is used to establish a Stone-like representation theorem conjectured by G. Grätzer and to find all equational subclasses of the class of pseudocomplemented distributive lattices.

One of the most important results in the theory of decomposition of universal relational schemata is the equivalence of acyclicity of the hypergraph of the schema to numerous desirable properties regarding simplicity of constraints, correctness of query evaluation algorithms, and complexity of integrity maintenance. In this paper, we show that the thrust of these results is not specific to the ...

We give a complete description of subdirectly irreducible rings with involution satisfying x = x for some positive integer n. We also discuss ways to apply this result for constructing lattices of varieties of rings with involution obeying an identity of the given type. MSC 2000: 16W10, 08B26, 08B15