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...

For the Fr'{e}chet algebras $(A, (p_k))$ and $(B, (q_k))$ and $n in mathbb{N}$, $ngeq 2$, a linear map $T:A rightarrow B$ is called textit{almost $n$-multiplicative}, with respect to $(p_k)$ and $(q_k)$, if there exists $varepsilongeq 0$ such that$$q_k(Ta_1a_2cdots a_n-Ta_1Ta_2cdots Ta_n)leq varepsilon p_k(a_1) p_k(a_2)cdots p_k(a_n),$$for each $kin mathbb{N}$ and $a_1, a_2, ldots, a_nin A$. Th...

The model theory of metric structures ([?]) was successfully applied to analyze ultrapowers of C*-algebras in [?] and [?]. Since important classes of separable C*-algebras, such as UHF, AF, or nuclear algebras, are not elementary (i.e., not characterized by their theory—see [?, §6.1]), for a moment it seemed that model theoretic methods do not apply to these classes of C*-algebras. We prove res...

Let %? be a separable Hubert space and !T c 3§(J%f) be an algebra of bounded operators. Say F is triangular if ^ n ^ * is a maximal abelian self-adjoint subalgebra (m.a.s.a.) of 3B{%?) and call this m.a.s.a. the diagonal of J7". A triangular algebra is maximal triangular if it is not properly contained in any triangular algebra. Triangular algebras of operators have been studied for 30 years no...

in this paper, we  study the arens regularity properties of module actions. we investigate some properties of topological centers of module actions ${z}^ell_{b^{**}}(a^{**})$ and  ${z}^ell_{a^{**}}(b^{**})$ with some conclusions in group algebras.

in this paper the concept of an $omega$- almost boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $omega$- almost boolean ring over a locally boolean space.

We give the classification of (co-)path Hopf algebras and semi-path Hopf algebras with pointed module structures. This leads to the classification of multiple crown algebras and multiple Taft algebras as well as kG-Yetter-Drinfeld modules and Nichols algebras with pointed module structures. Moreover, we characterize quantum enveloping algebras in terms of semi-path Hopf algebras. 2000 Mathemati...

We give the classification of (co-)path Hopf algebras and semi-path Hopf algebras with pointed module structures. This leads to the classification of multiple crown algebras and multiple Taft algebras as well as pointed Yetter-Drinfeld kG-modules and the corresponding Nichols algebras. Moreover, we characterize quantum enveloping algebras in terms of semi-path Hopf algebras.

BCK and BCI-algebras, two classes of algebras of logic, were introduced by Imai and Iseki [1], Iseki [2] and Iseki and Tanaka [3] and have been extensively studied by various other researchers [4, 5]. It is known that the class of BCK-algebras is a proper subclass of the class of BCI-algebras. In [6, 7] a wider class of abstract algebras was introduced by Q.P.Hu and X.Li.They have shown that th...

We study an extension of MV algebras, called μMV algebras, in which minimal and maximal fixed points are definable. The first result is that μMV algebras are term-wise equivalent to divisible MV∆algebras, i.e. a combination of two known extensions of MV algebras: divisible MV algebras [4] and MV∆algebras [6]. Using methods from the two known extensions we derive a number of results about μMV al...