A Banach lattice algebra is a Banach lattice, an associative algebra with a sub-multiplicative norm and the product of positive elements should be positive. In this note we study the Arens regularity and cohomological properties of Banach lattice algebras.

In this paper, by using Gröbner-Shirshov bases, we show that in the following classes, each (resp. countably generated) algebra can be embedded into a simple (resp. two-generated) algebra: associative differential algebras, associative Ω-algebras, associative λ-differential algebras. We show that in the following classes, each countably generated algebra over a countable field k can be embedded...

G∞-structure is shown to exist on the deformation complex of a morphism of associative algebras. The main step of the construction is extension of a B∞-algebra by an associative algebra. Actions of B∞-algebras on associative and B∞-algebras are analyzed, extensions of B∞-algebras by associative and B∞-algebras, that they act upon, are constructed. The resulting G∞-algebra on the deformation com...

We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized projective geometries, where the former correspond to the Lie product of an associative algebra and the latter to its Jordan product. A further development of t...

The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a polarization of Hom-associative algebra leads to Hom-Jordan algebra. INTRODUCTION Hom-algebraic structures are algebras where the identities defining the st...

In this paper, we propose a new multi-comparand associative machine (MCA-machine) and its application to relational algebra operations. We first offer a new efficient associative algorithm for the multi-comparand parallel search. It generalizes the Falkoff associative algorithm that performs a parallel search in a matrix based on the exact match with a given pattern. Then we apply the new assoc...