The lattice of z-ideals of the ring C(X) of real-valued continuous functions on a completely regular Hausdorff space X has been shown by Mart́ınez and Zenk to be a complete Heyting algebra with certain properties. We show that these properties are due only to the fact that C(X) is an f -ring with bounded inversion. This we do by studying lattices of algebraic z-ideals of abstract f -rings with b...

A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...

Semi De Morgan algebras form a variety of normal distributive lattice expansions [7] introduced by H.P. Sankappanavar [16] as a common abstraction of De Morgan algebras and distributive pseudocomplemented lattices. A fully selfextensional logic SDM naturally arises from semi De Morgan algebras, which has been studied from a duality-theoretic perspective [13], from the perspective of canonical e...

Let α be an infinite ordinal. There are non-isomorphic representable algebras of dimension α each of which is a generating subreduct of the same β dimensional algebra. Dually there exists a representable algebra A of dimension , α such that A is a generating subreduct of B and , B′ however, B and B′ are not isomorphic. The above was proven to hold for infinite dimensional cylindric algebras (CA...

For a Heyting algebra A, we show that the following conditions are equivalent: (i) A is profinite; (ii) A is finitely approximable, complete, and completely joinprime generated; (iii) A is isomorphic to the Heyting algebra Up(X) of upsets of an image-finite poset X. We also show that A is isomorphic to its profinite completion iff A is finitely approximable, complete, and the kernel of every fi...