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La idea de construir una álgebra que expresara matemáticamente propiedades for­males de conceptos lógicos tiene hoy más de un siglo. En 1847 G. Boole presentó un sis­tema algebraico asociable al cálculo de conect...

In this book we present and study some problems of Measure Theories in Boolean algebra and their possible generalizations to effect on algebras which are weaker structures.

El estudio de la MV-álgebras tiene una gran importancia en el contexto del álgebra, ya que, además de su relación con las lógicas multivaluadas, también se vincula con otros contextos relevantes de este campo, como...

Trata de álgebras ponderadas no necesariamente ponderativas, esto es, train algebras.

The following open problem state that: If  is a dense range homomorphism from Banach algebra into Banach algebra  such that  is semisimple. Is  automatically continuous? (see[1]) In [5] given a partial solution of th...

In this paper we investigate a subvariety BA of tense algebras, which we call Boolean algebras with a distinguished automorphism. This variety provides a unifying framework for the algebras studied by Monteiro in [4] and...

We establish the conjugacy of Cartan subalgebras for extended affine Lie algebras whose centreless core is “of type A”, i.e., ℓ×ℓ-matrices over a quantum torus Q whose trace lies in the commutator space of Q. Th...

Abstract Advanced mathematical tools are used to conduct research on the kinematics analysis of hybrid mechanisms, and the generalized analysis method and concise kinematics transfer matrix are obtained. In this study, f...

We complete the classification of Hopf algebras of dimension 16 over an algebraically closed field of characteristic zero. We show that a non-semisimple Hopf algebra of dimension 16, has either the Chevalley property or ...

We generalize a result on the Heisenberg Lie algebra that gives restrictions to possible Lie bialgebra cobrackets on 2-step nilpotent algebras with some additional properties. For the class of 2-step nilpotent Lie algebr...

For each 1 ≤ p < ∞ and each countable oriented graph Q we introduce an L p -operator algebra O p (Q) which contains the Leavitt path C-algebra LQ as a dense subalgebra and is universal for those L p -representations ...

The following open problem stated that, if T: A⟶B is a dense range homomorphism between Banach algebras A and B such that B is semi-simple. Is T automatically continuous? (see [1]). In [3] given a partial solution of t...

In this paper we describe all the nilradicals of parabolic subalgebras of split real simple Lie algebras admitting symplectic structures.The main tools used to obtain this list are Kostant's description of the highest we...

Abstract In this paper we introduce and study a relation “~” between projections, a relation “ ” on positive operators and a relation "~G" (G-group) on projections in extended factor algebras. The main results in...

In this work we obtain all rigid complex 3-dimensional multiplicative Hom-Lie algebras. This is done by studying all deformations of multiplicative Hom-Lie algebras which are also Lie algebras. As a byproduct, we obtain ...

We consider a class of Nichols algebras B(Lq(1 , G)) introduced in Andruskiewitsch et al. which are domains and have many favourable properties like AS-regular and strongly noetherian. We classify their finite-dimensiona...

We show that the definition of unrolled Hopf algebras can be naturally extended to the Nichols algebra B(V) of a Yetter-Drinfeld module V on which a Lie algebra g acts by biderivations. As a special case, we find unrolle...

Distributive Hilbert algebras with infimum, or DH^-algebras for short, are algebras with implication and conjunction, in which the implication and the conjunction do not necessarily satisfy the residuation law. These alg...

We investigate the behavior of finitely generated projective modules over a down-up algebra. Specifically, we show that every noetherian down-up algebra A(α,β,γ) has a non-free, stably free right ideal. Further, we co...

In this paper we give a constructive proof that the variety of Boolean algebras has the strong amalgamation property by describing constructively the strong amalgams in the variety. Then, capitalizing on this constructio...

The finite model property of the variety of S-algebras was proved by X. Caicedo using Kripke model techniques of the associated calculus. A more algebraic proof, but still strongly based on Kripke model ideas, was given ...

In this paper we study the theory of cleft extensions for a weak bialgebra H. Among other results, we determine when two unitary crossed products of an algebra A by H are equivalent and we prove that if H is a weak Hopf ...

Let A be a von Neumann algebra and PA the manifold of projections in A. There is a natural linear connection in PA, which in the finite dimensional case coincides with the the Levi-Civita connection of the Grassmann mani...

In this paper, we develop a systematic framework for studying fixed-point theory in the setting of normed GE-algebras. Building on the GE-norm, we introduce and analyze nonexpansive mappings, α-averaged mappings, and en...