Some generalizations of BCI algebras (the RM, BH, CI, BCH,
 BH**, BCH**, and *aRM** algebras) satisfying the identity $(x \rightarrow
 1)\rightarrow y = (y \rightarrow 1) x$ are considered. The connections these algebras
 various commutative groups (such as, for
 example, involutive moons (weakly)
 goops) described. In particular, it is proved that an RM
 algebra v...

We characterize, classify and axiomatize all subvarieties of IMTL(3), the variety of IMTL-algebras given by the equation ¬(x3) ∨ x ≈ >. We also give a canonical set of generators for each one. Introduction and preliminaries An IMTL-algebra is a bounded residuated lattice A = 〈A,∧,∨, ∗,→,¬,⊥,>〉, where ∧ and ∨ are meet and join, 〈∗,→〉 is a residuated pair, ¬ is the associated negation (i.e. ¬x =d...

With any involutive anti-algebra and coalgebra automorphism of a quasitriangular bialgebra we associate a reflection equation algebra. A Hopf algebraic treatment of the reflection equation of this type and its universal solution is given. Applications to the twisted Yangians are considered.

Let X be a non-degenerate left Banach module over a normed algebra A having a bounded approximate left identity. We show that, if A is a left ideal of a larger algebra, then this representation can be extended to a representation of the larger algebra. Based on this result, we study in detail the existence and properties of representations of the various centralizer algebras of A which are comp...

Involutive bases are a special kind of non-reduced Gröbner bases. They have been introduced by Gerdt and collaborators for polynomial ideals (see e.g. Zharkov and Blinkov, 1993; Gerdt and Blinkov, 1998a,b) based on ideas from the Janet–Riquier theory of differential equations (Janet, 1929; Riquier, 1910). Involutive bases possess special combinatorial properties: in particular, they define Stan...

the notion of vague ideals in pseudo mv-algebras is introduced,and several properties are investigated. conditions for a vague set to be avague ideal are provided. conditions for a vague ideal to be implicative aregiven. characterizations of (implicative, prime) vague ideals are discussed.the smallest vague ideal containing a given vague set is established. primeand implicative extension proper...

Let X be a non-degenerate left Banach module over a normed algebra A having a bounded approximate left identity. We show that, if A is a left ideal of a larger algebra, then this representation can be extended to a representation of the larger algebra. Based on this result, we study in detail the existence and properties of representations of the various centralizer algebras of A which are comp...

Let $f : A rightarrow B$ be a ring homomorphism and $J$ an ideal of $B$. In this paper, we give a necessary and sufficient condition for the amalgamated algebra along an ideal $Abowtie^fJ$ to be $J$-Noetherian. Then we give a characterization for pseudo-irreducible ideals of $Abowtie^fJ$, in special cases.

We give a dimension bound on the irreducible components of the characteristic variety of a system of linear partial di.erential equations de0ned from a suitable 0ltration of the Weyl algebra An. This generalizes an important consequence of the fact that a characteristic variety de0ned from the order 0ltration is involutive. More explicitly, we consider a 0ltration of An induced by any vector (u...

Dendriform algebras are certain splitting of associative and arise naturally from Rota-Baxter operators, shuffle planar binary trees. In this paper, we first consider involutive dendriform algebras, their cohomology homotopy analogs. The an algebra splits the Hochschild algebra. next, introduce a more general notion oriented algebras. We develop theory for that closely related to extensions gov...