According to a result by K. B. Lee, the lattice of varieties of pseudocomplemented distributive lattices is the ui + 1 chain B_i C Bo C Bi C • ■ ■ C Bn C •■ • C Bw in which the first three varieties are formed by trivial, Boolean, and Stone algebras respectively. In the present paper it is shown that any Stone algebra is determined within Bi by its endomorphism monoid, and that there are at mos...

In this article we study two different generalizations of von Neumann regularity, namely strong topological regularity and weak regularity, in the Banach algebra context. We show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. Then we consider strong topological regularity of certain concrete algebras. Moreover we obtain ...

We show that if a subgroup of the automorphism group Fraïssé limit finite Heyting algebras has countable index, then it lies between pointwise and setwise stabilizer some set.

We present a category equivalent to that of semi-Nelson algebras. The objects in this are pairs consisting semi-Heyting algebra and one its filters. filters must contain all the dense elements satisfy an additional technical condition. also show case dually hemimorphic algebras, not necessary is

let  and  be banach algebras, ,  and . we define an -product on  which is a strongly splitting extension of  by . we show that these products form a large class of banach algebras which contains all module extensions and triangular banach algebras. then we consider spectrum, arens regularity, amenability and weak amenability of these products.

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...

It is well-known that congruences on a Heyting algebra are in one-to-one correspondence with filters of the underlying lattice. If an algebra A has a Heyting algebra reduct, it is of natural interest to characterise which filters correspond to congruences on A. Such a characterisation was given by Hasimoto [1]. When the filters can be sufficiently described by a single unary term, many useful p...

Let  and  be Banach algebras, ,  and . We define an -product on  which is a strongly splitting extension of  by . We show that these products form a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Then we consider spectrum, Arens regularity, amenability and weak amenability of these products.