Although every computable data type has an initial algebra speci-cation with hidden functions, it may happen that some of the homo-morphic images of the data type are not models of the speciication. The latter are reducts of algebras that would be models of the specii-cation if all its functions were visible, whereas the homomorphic images of the data type are independent of the speciication an...

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 define $varphi$-Connes module amenability of a dual Banach algebra $mathcal{A}$ where $varphi$ is a bounded $w_{k^*}$-module homomorphism from $mathcal{A}$ to $mathcal{A}$. We are mainly concerned with the study of $varphi$-module normal virtual diagonals. We show that if $S$ is a weakly cancellative inverse semigroup with subsemigroup $E$ of idemp...

For a real reductive dual pair the Capelli identities define a homomorphism C from the center of the universal enveloping algebra of the larger group to the center of the universal enveloping algebra of the smaller group. In terms of the Harish-Chandra isomorphism, this map involves a ρ-shift. We view a dual pair as a Lie supergroup and offer a construction of the homomorphism C based solely on...

A Riemann-Lie algebra is a Lie algebra G such that its dual G∗ carries a Riemannian metric compatible (in the sense introduced by the author in C. R. Acad. Sci. Paris, t. 333, Série I, (2001) 763–768) with the canonical linear Poisson structure of G∗ . The notion of Riemann-Lie algebra has its origins in the study, by the author, of Riemann-Poisson manifolds (see Differential Geometry and its A...

The loop homology of a closed orientable manifoldM of dimensionm is the commutative algebra H∗(LM) = H∗+m(LM) equipped with the Chas-Sullivan loop product. Here LM denotes the free loop on M . There is also a homomorphism of graded algebras I from H∗(LM) to the Pontryagin algebra H∗(ΩM). The primary purpose of this paper is to study the loop homology and the homomorphism I, when M is a fibered ...

We show that the tree-level part of a theory of finite type invariants of 3-manifolds (based on surgery on objects called claspers, Y-graphs or clovers) is essentially given by classical algebraic topology in terms of the Johnson homomorphism and Massey products, for arbitrary 3-manifolds. A key role of our proof is played by the notion of a homology cylinder, viewed as an enlargement of the ma...

let φ be a w  -continuous homomorphism from a dual banach algebra to c. the notion of φ-connes amenability is studied and some characterizations is given. a type of diagonal for dual banach algebras is dened. it is proved that the existence of such a diagonal is equivalent to φ-connes amenability. it is also shown that φ-connes amenability is equivalent to so-called φ-splitting of a certain s...

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.