A noncommutative algebra A, called an algebraic noncommutative geometry, is defined, with a parameter ε in the centre. When ε is set to zero, the commutative algebra A0 of algebraic functions on an algebraic manifold M is obtained. This A0 is a subalgebra of Cω(M), which is dense if M is compact. The generators of A define an immersion of M into Rn, and M inherits a Poisson structure as the lim...

–a notion of amenability for topological semigroups is introduced. a topological semigroup s iscalled johnson amenable if for every banach s -bimodule e , every bounded crossed homomorphism froms to e* is principal. in this paper it is shown that a discrete semigroup s is johnson amenable if and only if1(s) is an amenable banach algebra. also, we show that if a topological semigroup s is johns...

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.

In the group of (continuous) Jordan automorphisms, with the uniform topology, on a semisimple Banach algebra, we show that the connected component of the identity consists of automorphisms. P. Civin and B. Yood have shown that a Jordan homomorphism (that is, a homomorphism that preserves the product xoy = | (xy+yx)) from a Banach algebra onto a semisimple Banach algebra is continuous provided t...

A basic problem in the theory of Lie algebra extensions concerns a given homomorphism x of a Lie algebra L into the Lie algebra of outer derivations of a Lie algebra B . In analogy with the theory of group extensions, Mori and HochschiId developed the concept of an obstruction to x being the homomorphism defined by some Lie algebra extension of B by L . This note considers an alternative approa...

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.

In this paper, applying the concept of generalized A-valued norm on a right $H^*$-module and also the notion of ϕ-homomorphism of Finsler modules over $C^*$-algebras we first improve the definition of the Finsler module over $H^*$-algebra and then define ϕ-morphism of Finsler modules over $H^*$-algebras. Finally we present some results concerning these new ones.

For an endofunctor H an initial algebra I has, by Lambek’s Lemma, invertible structure map, thus, it can be considered as a coalgebra. We call an H-coalgebra wellfounded if it has a coalgebra homomorphism into I. This is equivalent to the wellfoundedness in Taylor’s “Practical Foundations”, defined by means of an induction principle. And it is also equivalent to the recursivity studied by Capre...