in this paper, we introduce a class of rings which is a generalization of reversible rings. let r be a ring with identity. a ring r is called central reversible if for any a,b ∈ r, ab=0 implies ba belongs to the center of r. since every reversible ring is central reversible, we study sufficient conditions for central reversible rings to be reversible. we prove that some results of reversible ri...

In a paper by Xu, some simple Lie algebras of generalized Cartan type were constructed, using the mixtures of grading operators and down-grading operators. Among them, are the simple Lie algebras of generalized Witt type, which are in general nongraded and have no torus. In this paper, some representations of these simple Lie algebras of generalized Witt type are presented. 1. INTRODUCTION The ...

in this paper we focus on a special class of commutative local‎ ‎rings called spap-rings and study the relationship between this‎ ‎class and other classes of rings‎. ‎we characterize the structure of‎ ‎modules and especially‎, ‎the prime submodules of free modules over‎ ‎an spap-ring and derive some basic properties‎. ‎then we answer the‎ ‎question of lam and reyes about strongly oka ideals fam...

Commutative Gröbner Bases are a well established technique with many applications, including polynomial solving and constructive approaches to commutative algebra and algebraic geometry. Noncommutative Gröbner Bases are a focus of much recent research activity. For example, combining invariant theory and elimination theory, or elimination in moving frames of partial differential operators invar...

Differential calculi of Poincaré-Birkhoff-Witt type on universal enveloping algebras of Lie algebras g are defined. This definition turns out to be independent of the basis chosen in g. The role of automorphisms of g is explained. It is proved that no differential calculus of PoincaréBirkhoff-Witt type exists on semi-simple Lie algebras. Examples are given, namely gln, Abelian Lie algebras, the...

The Witt group of smooth real projective curves was first computed by Knebusch in [Kn]. If the curve is not complete but still smooth, the Witt group is also studied in [Kn] but not explicitely calculated. However, for some precise examples of smooth affine curves, we may find explicit calculations ([Knu] and [Ay-Oj]). In this paper, the Witt group of a general smooth curve is explicitely calcu...

Generalizing and synthesizing earlier work on the model theory of valued difference fields and on the model theory of valued fields with analytic structure, we prove Ax-Kochen-Eršov style relative completeness and relative quantifier elimination theorems for a theory of valuation rings with analytic and difference structure. Specializing our results to the case of W [F p ], the ring of Witt vec...

The purpose of this paper is to count the number of isomorphism types of reduced Witt rings of nondegenerate symmetric bilinear forms over fields with a fixed number of orderings. All of the background material necessary for understanding the situation in which this counting problem arises will be described in Section 1. Using results from [2], this problem is restated in Section 2 in terms of ...

This is a foundational account of the étale topology of generalized Witt vectors and of related constructions. The theory of the usual, “p-typical” Witt vectors of p-adic schemes of finite type is already reasonably well developed. The main point here is to generalize this theory in two different ways. We allow not just p-typical Witt vectors but also, for example, those taken with respect to a...

The paper addresses the quantization of minisuperspace cosmological models, with application to the Taub Model. By desparametrizing the model with an extrinsic time, a formalism is developed in order to define a conserved Schrödinger inner product in the space of solutions of the Wheeler-De Witt equation. A quantum version of classical canonical transformations is introduced for connecting the ...