Given two determinantal rings over a field k, we consider the Rees algebra of the diagonal ideal, the kernel of the multiplication map. The special fiber ring of the diagonal ideal is the homogeneous coordinate ring of the secant variety. When the Rees algebra and the symmetric algebra coincide, we show that the Rees algebra is CohenMacaulay.

We study the class of Bernstein algebras that are algebraic, in sense each element generates a finite-dimensional subalgebra. Every algebra has maximal algebraic ideal, and quotient is zero-multiplication algebra. Several equivalent conditions for to be given. In particular, known characterizations train terms nilpotency generalized case locally algebras. Along way, we show if Banach (respectiv...

in this paper, we study the arens regularity properties of module actions and we extend some proposition from baker, dales, lau and others into general situations. we establish some relationships between the topological centers of module actions and factorization properties of them with some results in group algebras. in 1951 arens shows that the second dual of banach algebra endowed with the e...

The main purpose of this article is to study pro-p groups with quadratic Fp-cohomology algebra, i.e. H•-quadratic groups. Prime examples such are the maximal Galois fields containing a primitive root unity order p. We show that amalgamated free product and HNN-extension H•-quadratic, under certain necessary conditions. Moreover, we introduce investigate new family yields many groups: p-RAAGs. T...

Let Pn := K[x1, . . . , xn] be a polynomial algebra over a field K of characteristic zero. The Jacobian algebra An is the subalgebra of EndK(Pn) generated by the Weyl algebra An := D(Pn) = K〈x1, . . . , xn, ∂1, . . . , ∂n〉 and the elements (∂1x1) −1, . . . , (∂nxn) −1 ∈ EndK(Pn). The algebra An appears naturally in study of the group of automorphisms of Pn. The algebra An is large since it cont...

We fuzzify the concept of an associative -ideal in an IS-algebra. We give a relation between a fuzzy -ideal and a fuzzy associative -ideal, and we investigate some related properties.

The theory of Amalgamated Knowledge' Bases [7] represents a formal logical foundation for heterogeneous databases. In an Amalgamated Knowledge Base, data sources are modeled by generalized annotated logic. Moreover, an Amalgamated Knowledge Base is equipped with a supervisor acting as a mediator for amalgamating knowledge from the local databases. Even if the framework is quite appealing, it do...

If X,Y are normed spaces, let B(X,Y ) be the set of all bounded linear maps X → Y . If T : X → Y is a linear map, I take it as known that T is bounded if and only if it is continuous if and only if E ⊆ X being bounded implies that T (E) ⊆ Y is bounded. I also take it as known that B(X,Y ) is a normed space with the operator norm, that if Y is a Banach space then B(X,Y ) is a Banach space, that ...

In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal m...