Let  be a Banach algebra. Let  be linear mappings on . First we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple Banach algebras, in certain case. Afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

In [6] S. Shelah showed that in the endomorphism semi-group of an infinitely generated algebra which is free in a variety one can interpret some set theory. It follows from his results that, for an algebra Fκ which is free of infinite rank κ in a variety of algebras in a language L, if κ" rLr, then the first-order theory of the endomorphism semi-group of Fκ, Th(End(Fκ)), syntactically interpret...

The Semi Heyting Almost Distributive Lattice (SHADL) is a mathematical framework that combines the concepts of semi algebra and almost distributive lattice. This abstract highlights applications SHADL in various domains

For the root system of each complex semi-simple Lie algebra of rank two, and for the associated 2D Toda chain E = {

In this paper authors have given a separation theorem for α ideals in a 0distributive lattice. Some characterizations of semi prime ideals have been discussed. Then they have included an interesting result on *-ideals in a p-algebra by using the properties of semi prime ideals.

Differing from [6] this paper reduces non-linear ranking function discovering for polynomial programs to semi-algebraic system solving, and demonstrates how to apply the symbolic computation tools, DISCOVERER and QEPCAD, to some interesting examples. keywords: Program Verification, Loop Termination, Ranking Function, Polynomial Programs, Semi-Algebraic Systems, Computer Algebra, DISCOVERER, QEPCAD

The notion of vertex operator algebra ([B], [FHL], [FLM]) is the algebraic counterpart of the notion of what is now usually called “chiral algebra” in conformal field theory, and vertex operator algebra theory generalizes the theories of affine Lie algebras, the Virasoro algebra and representations (cf. [B], [DL], [FLM], [FZ]). It has been well known (cf. [FZ], [L1]) that the irreducible highes...

We prove that the operator Hilbert space OH does not embed completely isomorphically into the predual of a semi-finite von Neumann algebra. This complements Junge’s recent result that it admits such an embedding in the non semi-finite case. ——————– In remarkable recent work [5], Marius Junge proves that the operator Hilbert space OH (from [8], see also [9]) embeds completely isomorphically (c.i...

‎In this paper‎, ‎we introduce the notion of the radical of a $PMV$-algebra $A$ and we charactrize radical $A$ via elements of $A$‎. ‎Also‎, ‎we introduce the notion of the radical of a $cdot$-ideal in $PMV$-algebras‎. ‎Several characterizations of this radical is given‎. ‎We define the notion of a semimaximal $cdot$-ideal in a $PMV$-algebra‎. ‎Finally we show that $A/I$ has no nilpotent elemen...