By constructing explicit examples, we show that the core of a group-like element in cocommutative cosemisimple Yetter-Drinfel'd Hopf algebra over group ring finite abelian is not always completely trivial.

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...

The question of whether a hypercyclic operator T acting on Fréchet algebra X admits or not an vectors (but 0) has been addressed in the recent literature. In this paper we give new criteria and characterisations context convolution operators H(C) backward shifts general sequence algebra. Analogous questions arise for stronger properties like frequent hypercyclicity. trend sufficient condition w...

| Constraint relational databases use constraints to both model and query data. A constraint relation contains a nite set of generalized tuples. Each generalized tuple is represented by a conjunction of constraints on a given logical theory and, depending on the logical theory and the speciic conjunction of constraints, it may possibly represent an in-nite set of relational tuples. For their ch...

In this paper we obtained for the Higgs algebra three kinds of single-mode realizations such as the unitary Holstein-Primakoff-like realization, the non-unitary Dyson-like realization and the unitary realization based upon Villain-like realization. The corresponding similarity transformations between the Holstein-Primakoff-like realizations and the Dyson-like realizations are revealed. PACS: 11...

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...

We consider quantum dynamical systems whose degrees of freedom are described by N × N matrices, in the planar limit N → ∞. Examples are gauge theories and the M(atrix)-theory of strings. States invariant under U(N) are 'closed strings', modelled by traces of products of matrices. We have discovered that the U(N)-invariant operators acting on both open and closed string states form a remarkable ...

A bstract Conformal Carroll symmetry generically arises on null manifolds and is important for holography of asymptotically flat spacetimes, generic black hole horizons tensionless strings. In this paper, we focus two dimensional (2 d ) hence the 2 or equivalently 3 Bondi-Metzner-Sachs (BMS) algebra. Using covariance, write most general free massless scalar field theory discover three inequival...

It is common knowledge that the construction of one-parameter deformations of various algebraic structures, like associative algebras or Lie algebras, involves certain conditions on cohomology classes, and that these conditions are usually expressed in terms of Massey products, or rather Massey powers. The cohomology classes considered are those of certain differential graded Lie algebras (DGLA...