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.

Let $nin mathbb{N}$. An additive map $h:Ato B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $ain A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$. For these cases, every involutive $n$-Jordan homomorphism between commutative C-algebras is norm continuous.

these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...

Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra‎. ‎In this paper‎, ‎we investigate Gorenstein global dimensions for Hopf‎ ‎algebras and twisted smash product algebras $Astar H$‎. ‎Results from‎ ‎the literature are generalized‎. 

Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpoten...

in this paper, we classify the indecomposable non-nilpotent solvable lie algebras with $n(r_n,m,r)$ nilradical,by using the derivation algebra and the automorphism group of $n(r_n,m,r)$.we also prove that these solvable lie algebras are complete and unique, up to isomorphism.

in the present paper we give a partially negative answer to a conjecture of ghahramani, runde and willis. we also discuss the derivation problem for both foundation semigroup algebras and clifford semigroup algebras. in particular, we prove that if s is a topological clifford semigroup for which es is finite, then h1(m(s),m(s))={0}.

almost multiplier is rather a new concept in the theory of almost functions. in thispaper we discuss on the boundedness of almost multipliers on some special banach algebras,namely stable algebras. we also de ne an adjoint and extension for almost multiplier.

in this paper, the main results are:a study of the finitely generated mv-algebras of continuous functions from the n-th power of the unit real interval i to i;a study of hopfian mv-algebras; anda category-theoretic study of the map sending an mv-algebra as above to the range of its generators (up to a suitable form of homeomorphism).

In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...