Recall that a commutative ring R is said to be a pseudo-valuation ring if every prime ideal of R is strongly prime. We define a completely pseudovaluation ring. Let R be a ring (not necessarily commutative). We say that R is a completely pseudo-valuation ring if every prime ideal of R is completely prime. With this we prove that if R is a commutative Noetherian ring, which is also an algebra ov...

let $a$ be a banach algebra and $x$ be a banach $a$-bimodule. then ${mathcal{s}}=a oplus x$, the $l^1$-direct sum of $a$ and $x$ becomes a module extension banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ in this paper, we investigate biflatness and biprojectivity for these banach algebras. we also discuss on automatic continuity of derivations on ${mathcal{s...

Let G be a locally compact group, 1 < p < ∞ and let ω be a weight function on G. Recently, we introduced the Lebesgue weighted L−algebra L ω (G). Here, we establish necessary and sufficient conditions for L ω (G) to be φ−contractible, pseudo-contractible or contractible. Moreover we give some similar results about L(G,ω).

Let G be a Poisson–Lie group equipped with left invariant contravariant pseudo-Riemannian metric. There are many ways to lift the Poisson structure on tangent bundle TG of G. In this paper, we induce metric TG, and express in different cases Levi-Civita connection curvature terms We prove that space differential forms Ω*(G) is graded algebra if, only Ω*(TG) algebra. Moreover, show Sanchez de Al...

In the paper [8], we introduced the notions of pseudo-hyperplane and pseudoembedding of a point-line geometry and proved that every generalized quadrangle of order (s, t), 2 ≤ s <∞, has faithful pseudo-embeddings. The present paper focuses on generalized quadrangles of order (3, t). Using the computer algebra system GAP [12] and invoking some theoretical relationships between pseudo-hyperplanes...

Boolean constraints play an important role in various constraint logic programming languages. In this paper we consider pseudo-Boolean constraints, that is equations and inequalities between pseudo-Boolean functions. A pseudoBoolean function is an integer-valued function of Boolean variables and thus a generalization of a Boolean function. Pseudo-Boolean functions occur in many application area...

We construct cocycles on the Lie algebra of pseudoand q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A “quantum” Godbillon-Vey cocycle on (pseudo)differential operators appears in this construction as a natural generalization of the Gelfand-Fuchs 3-cocycle on periodic vector fields. We describe a nontrivial embed...

We construct cocycles on the Lie algebra of pseudoand q-pseudodifferential symbols of one variable and on their close relatives: the sine-algebra and the Poisson algebra on two-torus. A ``quantum'' Godbillon Vey cocycle on (pseudo)differential operators appears in this construction as a natural generalization of the Gelfand Fuchs 3-cocycle on periodic vector fields. A nontrivial embedding of th...

Tossing a coin is the most elementary Monte-Carlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not capable of imitating a fair coin: pseudo random coins show more ‘‘heads’’ than ‘‘tails.’’ This bias explains the empirically observed failure of some random numbe...