We are exploring a scheme that allows optimizing queries over object-oriented databases with encapsulated behavior. Objects and classes will be able to reveal their behavior in terms of expressions in an algebraic language interpreted by a structural object-oriented database system. An object or class can agree or refuse to reveal its behavior. The structural algebra is richer than relational a...

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...

In this paper, we show that every surjective $n$-homomorphism ($n$-anti-homomorphism) from a Banach algebra $A$ into a semisimple Banach algebra $B$ is continuous.

When I first encountered abstract algebra in the late 1960s, I was drawn to its power and beauty. One of the liberating ideas of the subject is that in dealing with algebraic structures, you don’t need to worry about what the objects are; rather, it is how they behave that is important. Algebra is a wonderful language for describing the behavior of mathematical objects. My fascination with alge...

W hen I first encountered abstract algebra in the late 1960s, I was drawn to its power and beauty. One of the liberating ideas of the subject is that in dealing with algebraic structures, you do not need to worry about what the objects are; rather, it is how they behave that is important. Algebra is a wonderful language for describing the behavior of mathematical objects. My fascination with al...

The dater equalities constitutes an appropriate tool which allows a linear description of Timed Event Graphs in the field of (max, +) algebra. This paper proposes an equivalent model in the usual algebra which can describe Timed and P-time Event Graphs. Considering 1-periodic behavior, the application of a variant of Farkas’ lemma allows the determination of upper and lower bounds of the produc...

Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...

In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$  associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $  C^* $-algebra  $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...

we present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. first, we introduce a hyper bck-algebra induced by a max-min general fuzzy automaton. then, we study the properties of this hyper bck-algebra. particularly, some theorems and results for hyper bck-algebra are proved. for example, it is shown that this structure consists of different ty...