scholarly journals The number of torsion divisors in a strongly F-regular ring is bounded by the reciprocal of F-signature

2021 ◽  
pp. 1-11
Author(s):  
I. Martin
Keyword(s):  
Regular Ring

Analysis of Lattice Single Layer Cylindrical Structures

1987 ◽  
Vol 2 (2) ◽  
pp. 87-91 ◽  
Author(s):  
Istvan HegedüS
Keyword(s):  
Stress Distribution ◽  
Matrix Method ◽  
Regular Ring ◽  
Lattice Structure ◽  
Single Layer ◽  
Cylindrical Structures ◽  
Lattice Construction

A matrix method is presented for the calculation of bar forces in a single layer lattice cylinder composed of regular ring polygons and symmetrically arranged bracing bars. Substantial differences occur between the stress distribution in the lattice structure and that of the membrane cylinder under the same load. Therefore, a membrane cylinder cannot be considered as a replacement continuum for the lattice construction. The purpose of the paper is to draw attention to the danger in the utilisation, without due caution, of this analogy.

scholarly journals RINGS OF DEFINABLE SCALARS OF VERMA MODULES

2007 ◽  
Vol 06 (05) ◽  
pp. 779-787 ◽  
Author(s):  
SONIA L'INNOCENTE ◽  
MIKE PREST
Keyword(s):  
Lie Algebra ◽  
Model Theory ◽  
Regular Ring ◽  
Verma Module ◽  
Closed Field ◽  
Verma Modules ◽  
Von Neumann Regular Ring ◽  
Von Neumann ◽  
Canonical Map ◽  
Von Neumann Regular

Let M be a Verma module over the Lie algebra, sl 2(k), of trace zero 2 × 2 matrices over the algebraically closed field k. We show that the ring, RM, of definable scalars of M is a von Neumann regular ring and that the canonical map from U( sl 2(k)) to RM is an epimorphism of rings. We also describe the Ziegler closure of M. The proofs make use of ideas from the model theory of modules.

scholarly journals Commutative von Neumann regular rings are 1-Gröbner

2021 ◽  
pp. 30-30
Author(s):  
Zoran Petrovic ◽  
Maja Roslavcev
Keyword(s):  
Regular Ring ◽  
Finitely Generated ◽  
Von Neumann Regular Ring ◽  
Von Neumann ◽  
Von Neumann Regular Rings ◽  
Von Neumann Regular ◽  
Ring Of Polynomials ◽  
Bner Basis ◽  
Regular Rings

Let R be a commutative von Neumann regular ring. We show that every finitely generated ideal I in the ring of polynomials R[X] has a strong Gr?bner basis. We prove this result using only the defining property of a von Neumann regular ring.

RINGS OVER WHICH COEFFICIENTS OF NILPOTENT POLYNOMIALS ARE NILPOTENT

2011 ◽  
Vol 21 (05) ◽  
pp. 745-762 ◽  
Author(s):  
TAI KEUN KWAK ◽  
YANG LEE
Keyword(s):  
Polynomial Ring ◽  
Regular Ring ◽  
Von Neumann Regular Ring ◽  
Von Neumann ◽  
Nilpotent Elements ◽  
Von Neumann Regular ◽  
Armendariz Rings ◽  
Ring Extensions ◽  
Nil Ring

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, observing the structure of nilpotent elements in Armendariz rings and introducing the notion of nil-Armendariz rings. The class of nil-Armendariz rings contains Armendariz rings and NI rings. We continue the study of nil-Armendariz rings, concentrating on the structure of rings over which coefficients of nilpotent polynomials are nilpotent. In the procedure we introduce the notion of CN-rings that is a generalization of nil-Armendariz rings. We first construct a CN-ring but not nil-Armendariz. This may be a base on which Antoine's theory can be applied and elaborated. We investigate basic ring theoretic properties of CN-rings, and observe various kinds of CN-rings including ordinary ring extensions. It is shown that a ring R is CN if and only if R is nil-Armendariz if and only if R is Armendariz if and only if R is reduced when R is a von Neumann regular ring.

Factor-Correspondences in Regular Rings

1982 ◽  
Vol 34 (1) ◽  
pp. 23-30
Author(s):  
S. K. Berberian
Keyword(s):  
Present Article ◽  
Regular Ring ◽  
Decomposition Theorem ◽  
Matrix Rings ◽  
Basic Properties ◽  
Principal Ideals ◽  
Highly Effective ◽  
Left Factor ◽  
Regular Rings

Factor-correspondences are nothing more than a way of describing isomorphisms between principal ideals in a regular ring. However, due to a remarkable decomposition theorem of M. J. Wonenburger [7, Lemma 1], they have proved to be a highly effective tool in the study of completeness properties in matrix rings over regular rings [7, Theorem 1]. Factor-correspondences also figure in the proof of D. Handelman's theorem that an ℵ0-continuous regular ring is unitregular [4, Theorem 3.2].The aim of the present article is to sharpen the main result in [7] and to re-examine its applications to matrix rings. The basic properties of factor-correspondences are reviewed briefly for the reader's convenience.Throughout, R denotes a regular ring (with unity).Definition 1 (cf. [5, p. 209ff], [7, p. 212]). A right factor-correspondence in R is a right R-isomorphism φ : J → K, where J and K are principal right ideals of R (left factor-correspondences are defined dually).

Tensor Products of Dimension Groups and K0 of Unit-Regular Rings

1986 ◽  
Vol 38 (3) ◽  
pp. 633-658 ◽  
Author(s):  
K. R. Goodearl ◽  
D. E. Handelman
Keyword(s):  
Regular Ring ◽  
Hausdorff Space ◽  
Tensor Products ◽  
Matrix Algebras ◽  
Dimension Group ◽  
Grothendieck Groups ◽  
Dimension Groups ◽  
Direct Limits ◽  
Finite Products ◽  
Regular Rings

We study direct limits of finite products of matrix algebras (i.e., locally matricial algebras), their ordered Grothendieck groups (K0), and their tensor products. Given a dimension group G, a general problem is to determine whether G arises as K0 of a unit-regular ring or even as K0 of a locally matricial algebra. If G is countable, this is well known to be true. Here we provide positive answers in case (a) the cardinality of G is ℵ1, or (b) G is an arbitrary infinite tensor product of the groups considered in (a), or (c) G is the group of all continuous real-valued functions on an arbitrary compact Hausdorff space. In cases (a) and (b), we show that G in fact appears as K0 of a locally matricial algebra. Result (a) is the basis for an example due to de la Harpe and Skandalis of the failure of a determinantal property in a non-separable AF C*-algebra [18, Section 3].

On a Sheaf of Division Rings*

1975 ◽  
Vol 17 (5) ◽  
pp. 727-731
Author(s):  
George Szeto
Keyword(s):  
Principal Ideal ◽  
Regular Ring ◽  
Central Idempotent ◽  
Division Rings ◽  
Maximal Ideals ◽  
Strongly Regular ◽  
Th 1

R. Arens and I. Kaplansky ([1]) call a ring A biregular if every two sided principal ideal of A is generated by a central idempotent and a ring A strongly regular if for any a in A there exists b in A such that a=a2b. In ([1], Sections 2 and 3), a lot of interesting properties of a biregular ring and a strongly regular ring are given. Some more properties can also be found in [3], [5], [8], [9] and [13]. For example, J. Dauns and K. Hofmann ([3]) show that a biregular ring A is isomorphic with the global sections of the sheaf of simple rings A/K where K are maximal ideals of A. The converse is also proved by R. Pierce ([9], Th. 11–1). Moreover, J. Lambek ([5], Th. 1) extends the above representation of a biregular ring to a symmetric module.

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