Max-times algebra, sometimes known as subtropical algebra, is a semi-ring over the nonnegative real numbers where the addition operation is the max function and the multiplication is the standard one. Factorizing a nonnegative matrix over the maxtimes algebra, instead of the standard (nonnegative) one, allows us to find structures and regularities that cannot be easily expressed in the standard...

A class algebra has been used to model the query and data manipulation language for a prototype object-oriented database system which is being implemented for the WorldWide Web [7]. The Prolog prototype (i.e. operational semantics, if you will) is located at http : //www.cs.ccu.edu.tw/ ..~ dan/prologProgs/modeloo.t~t. The class algebra includes a Boolean algebra for class union, intersection, a...

Introduction. By a function algebra I shall mean a collection A of complex-valued functions on a set X such that the (pointwise) sum and the product of two functions in A are again in A. We shall always suppose that A contains the constant functions so that A becomes an algebra with unit over the field of complex numbers. A function algebra A is called self-ad joint if the complex conjugate of ...

we prove that rs-bl-algebras are mv-algebras.

let $mathcal{r}$ be a  commutative ring with identity, let $a$ and $b$ be two $mathcal{r}$-algebras and $varphi:blongrightarrow a$ be an $mathcal{r}$-additive algebra homomorphism. we introduce a new algebra $atimes_varphi b$, and give some basic properties of this algebra. generalized $2$-cocycle derivations on $atimes_varphi b$ are studied. accordingly, $atimes_varphi b$ is considered from th...

A class algebra has been used to model the query and data manipulation language for a prototype object-oriented database system which is being implemented for the WorldWide Web ?]. The Prolog prototype (i.e. operational semantics, if you will) is lo-dan=prologProgs=modeloo:txt. The class algebra includes a Boolean algebra for class union, intersection, and complement (i.e. diierence with any). ...

The space R comes with its standard topology which we denote byO (that is, O is the collection of open sets in R). It comes also with its Borel sigma algebra which we denote by B. The Borel sigma algebra is the smallest one containing all open sets (i.e., the sigma algebra generated by O). Let I be an arbitrary non-empty set (finite, countable or uncountable). For x ∈ I, the coordinate function...

Let $mathcal{R}$ be a  commutative ring with identity, let $A$ and $B$ be two $mathcal{R}$-algebras and $varphi:Blongrightarrow A$ be an $mathcal{R}$-additive algebra homomorphism. We introduce a new algebra $Atimes_varphi B$, and give some basic properties of this algebra. Generalized $2$-cocycle derivations on $Atimes_varphi B$ are studied. Accordingly, $Atimes_varphi B$ is considered from th...

The notion of computable function can be extended from the natural numbers to other domains, using an indexing. Usually, the choice of the indexing affects the set of computable functions and there is no intrinsic notion of computability over these domains. In this paper, we show that, in contrast, when we extend the notion of computable function to algebraic structures, we obtain an intrinsic ...

We introduce a pairing structure within the Moore complex NG of a simplicial group G and use it to investigate generators for N G n ∩ D n where D n is the subgroup generated by degenerate elements. This is applied to the study of algebraic models for homotopy types.