We define a tracial analog of the notion called sequentially split $$^*$$ -homomorphism between $$C^*$$ -algebras due to Barlak and Szabó show that several important approximation properties related classification theory pass from target algebra domain algebra. Then, we this framework arises Rokhlin finite group action an inclusion unital -algebras.

For the generality of fuzzy ideals in TM-algebra, a cubic ideal this algebra has been studied, such as and T-ideals. Some properties these are investigated. Also, we show that T-ideal is ideal, but converse not generally valid. In addition, sub-algebra defined, new relations between level subset discussed. After that, T-ideals under homomorphism image (pre-image) Finally, Cartesian product TM-a...

In this paper we study the concept of ph-biatness ofa Banach algebra A, where ph is a continuous homomorphism on A.We prove that if ph is a continuous epimorphism on A and A hasa bounded approximate identity and A is ph- biat, then A is ph-amenable. In the case where ph is an isomorphism on A we showthat the ph- amenability of A implies its ph-biatness.

The descent algebra of the symmetric group, over a field of non-zero characteristic p, is studied. A homomorphism into the algebra of generalised p-modular characters of the symmetric group is defined. This is then used to determine the radical, and its nilpotency index. It also allows the irreducible representations of the descent algebra to be described.

A Lie algebra gQ over Q is said to be R-universal if every homomorphism from gQ to gl(n,R) is conjugate to a homomorphism into gl(n,Q) (for every n). By using Galois cohomology, we provide a short proof of the known fact that every real semisimple Lie algebra has an R-universal Q-form. We also provide a classification of the R-universal Lie algebras that are semisimple.

A depth two extension A | B is shown to be weak depth two over its double centralizer V A (V A (B)) if this is separable over B. We introduce a notion of codepth two coalgebra homomorphism g : C → D, dual to a depth two algebra homomorphism. It is shown that the endomorphism ring of bicomodule endomorphisms End D C D forms a right bialgebroid over the centralizer subalgebra g * : D * → C * of t...

We investigate how a C*-algebra could consist of functions on a noncommutative set: a discretization of a C*-algebra A is a ∗-homomorphism A → M that factors through the canonical inclusion C(X) ⊆ `∞(X) when restricted to a commutative C*-subalgebra. Any C*-algebra admits an injective but nonfunctorial discretization, as well as a possibly noninjective functorial discretization, where M is a C*...

In this paper, we introduce an algebra H from a subspace lattice with respect to a fixed flag which contains its incidence algebra as a proper subalgebra. We then establish a relation between the algebra H and the quantum affine algebra Uq1/2(ŝl2), where q denotes the cardinality of the base field. It is an extension of the well-known relation between the incidence algebra of a subspace lattice...

A minimum depth is assigned to a ring homomorphism and a bimodule over its codomain. When the homomorphism is an inclusion and the bimodule is the codomain, the recent notion of depth of a subring in a paper by Boltje-Danz-Külshammer is recovered . Subring depth below an ideal gives a lower bound for BDK’s subring depth of a group algebra pair or a semisimple complex algebra pair.

We prove that, for a Poisson vertex algebra $${\cal V}$$ , the canonical injective homomorphism of variational cohomology to its classical is an isomorphism, provided that viewed as differential algebra, polynomials in finitely many variables. This theorem one key ingredients computation cohomology. For proof, we introduce sesquilinear Hochschild and Harrison complexes vanishing symmetric