The reticulation of an algebra was first defined for commutative rings by Simmons [19] and it was extended by Belluce to non-commutative rings [3]. As for the algebras of fuzzy logics, Belluce also constructed the reticulation of an MV-algebra [2], G. Georgescu defined the reticulation of a quantale [8] and L. Leuştean made this construction for BL-algebras [13, 14]. In each of the papers cited...

The notion of a linear space is generalized to the case where the underlying algebra is a commutative monoid and the set of scalars is a semiring reduct of a BL-algebra or an MValgebra. The notions of linear dependence and independence are also introduced and necessary and sufficient conditions when vectors form a basis of a semi-linear space are given. A linear mapping between two semilinear s...

We present some model theoretic results for Lukasiewicz predicate logic by using the methods of continuous model theory developed by Chang and Keisler. We prove compactness theorem with respect to the class of all structures taking values in the Lukasiewicz BL-algebra. We also prove some appropriate preservation theorems concerning universal and inductive theories. Finally, Skolemization and Mo...

We give an elementary proof of a result which characterizes onto *-isomorphisms of the algebra BL(H) of all the bounded linear operators on a Hilbert space H. A known proof of this result (Arveson, 1976) relies on the theory of irreducible representations of C∗-algebras, whereas the proof given by us is based on elementary properties of operators on a Hilbert space which can be found in any int...

My primary and current research work is in the general spirit of algebras of logic, lattice theory, hyper structures and applications. A partially ordered set, or poset for short is a pair (P, ≤) where P is a set and ≤ a partial order on P. A poset (P, ≤) is called a lattice if every pair x, y ∈ P has a least upper bound x ∨ y and a greatest lowest bound x ∧ y in P. A lattice is bounded if it h...

It is well-known that the second homology group H2(stn(R)) of the Steinberg Lie algebra stn(R) is trivial when n ≥ 5. In this paper, we will work out H2(stn(R)) explicitly for n = 3, 4 which are not necessarily trivial. Consequently, we obtained H2(sln(R)) for n = 3, 4. Introduction Steinberg Lie algebras stn(R) and/or their universal coverings have been studied by Bloch [Bl], Kassel-Loday [KL]...