For families of orthogonal and symplectic types quantum matrix (QM-) algebras, we derive corresponding versions of the Cayley-Hamilton theorem. For a wider family of BirmanMurakami-Wenzl type QM-algebras, we investigate a structure of its characteristic subalgebra (the subalgebra in which the coefficients of characteristic polynomials take values). We define 3 sets of generating elements of the...

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

A reductive Lie algebra g is one that can be written C(g) ⊕ [g,g], where C(g) denotes the center of g. Equivalently, for any ideal a, there is another ideal b such that g = a⊕ b. A Cartan subalgebra of g is a subalgebra h that is maximal with respect to being abelian and having ad X being semisimple for all X ∈ h. For a reductive group, h = C(g) ⊕ h′, where h′ is a Cartan subalgebra of the semi...

This paper introduces the concept of subalgebra and discusses some properties subalgebra. We also examine different types ideals how they behave. describe a homomorphism. Finally, we present quotient algebra discuss isomorphism theorems.

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...

We present an algebraic approach to string theory, using a Hamiltonian reduction of N = 2 WZW models. An embedding of sl(1|2) in a Lie superalgebra determines a niltopent subalgebra. Chirally gauging this subalgebra in the corresponding WZW action leads to an extension of the N = 2 superconformal algebra. We classify all the embeddings of sl(1|2) into Lie superalgebras: this provides an exhaust...

We show that “every countable algebra with a nonfinitely generated subalgebra has a maximal nonfinitely generated subalgebra” is provably equivalent to ’1-CA0 over RCA0.