By analyzing how one obtains the Stone space of the reduced product of an indexed collection of Boolean algebras from the Stone spaces of those algebras, we derive a topological construction, the "reduced coproduct", which makes sense for indexed collections of arbitrary Tichonov spaces. When the filter in question is an ultrafilter, we show how the "ultracoproduct" can be obtained from the usu...

By considering the notion of MV-algebras, we recall some results on enumeration of MV-algebras and wecarry out a study on characterization of MV-algebras of orders $2$, $3$, $4$, $5$, $6$ and $7$. We obtain that there is one non-isomorphic MV-algebra of orders $2$, $3$, $5$ and $7$ and two non-isomorphic MV-algebras of orders $4$ and $6$.

A locally compact group G is discrete if and only the Fourier algebra A(G) has a non-zero (weakly) multiplier. We partially extend this result to setting of ultraspherical hypergroups. Let H be an hypergroup let A(H) denote corresponding algebra. will give several characterizations discreteness in terms algebraic properties A(H). also study Arens regularity closed ideals

In this note the notion of interval-valued fuzzy B-algebras (briefly,i-v fuzzy B-algebras), the level and strong level B-subalgebra is introduced.Then we state and prove some theorems which determine the relationshipbetween these notions and B-subalgebras. The images and inverse images ofi-v fuzzy B-subalgebras are defined, and how the homomorphic images andinverse images of i-v fuzzy B-subalge...

the notion of $f$-derivations of up-algebras is introduced, some useful examples are discussed, and related properties are investigated. moreover, we show that the fixed set and the kernel of $f$-derivations are up-subalgebras of up-algebras,and also give examples to show that the two sets are not up-ideals of up-algebras in general.

let  and  be banach algebras, ,  and . we define an -product on  which is a strongly splitting extension of  by . we show that these products form a large class of banach algebras which contains all module extensions and triangular banach algebras. then we consider spectrum, arens regularity, amenability and weak amenability of these products.

we study the notion of bounded approximate connes-amenability for‎ ‎dual banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎we show that bounded approximate‎ ‎connes-amenability of dual banach algebras forces them to be unital‎. ‎for a separable dual banach algebra‎, ‎we prove that bounded‎ ‎approximate connes-amenability implies sequential approximate...

In this paper, we introduce a new algebraic structure, called a UP-algebra (UP means the University of Phayao) and a concept of UP-ideals, UP-subalgebras, congruences and UP-homomorphisms in UP-algebras, and investigated some related properties of them. We also describe connections between UP-ideals, UP-subalgebras, congruences and UP-homomorphisms, and show that the notion of UP-algebras is a ...