Rings With Involution Whose Symmetric Units Commute

1976 ◽  
Vol 28 (5) ◽  
pp. 915-928 ◽  
Author(s):  
Charles Lanski
Keyword(s):  
Unitary Group ◽  
Simple Ring ◽  
Algebraic Properties ◽  
Rings With Involution ◽  
Additional Assumptions

In the last few years many results have appeared which deal with questions of how various algebraic properties of the symmetric elements of a ring with involution, or the subring they generate, affect the structure of the whole ring. If the ring has an identity, similar questions may be posed by making assumptions about the symmetric units or subgroup they generate. Little seems to be known about the special units which exist in rings with involution, although several questions of importance have existed for some time. For example, given a simple ring with appropriate additional assumptions, is the unitary group essentially simple? Also, what can be said about the structure of subspaces invariant under conjugation by all unitary or symmetric units (see [7])?

Rings with Involution in which Every Trace is Nilpotent or Regular

1974 ◽  
Vol 26 (1) ◽  
pp. 130-137 ◽  
Author(s):  
Susan Montgomery
Keyword(s):  
Division Ring ◽  
Simple Ring ◽  
Direct Sum ◽  
Rings With Involution ◽  
Symmetric Element

A theorem of Marshall Osborn [15] states that a simple ring with involution of characteristic not 2 in which every non-zero symmetric element is invertible must be a division ring or the 2 × 2 matrices over a field. This result has been generalized in several directions. IfRis semi-simple and every symmetric element (or skew, or trace) is invertible or nilpotent, thenRmust be a division ring, the 2 × 2 matrices over a field, or the direct sum of a division ring and its opposite [6; 8; 13; 16].

scholarly journals Weighted Dual Covariance Moore-Penrose Inverses with respect to an Invertible Element inC*-Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Hesam Mahzoon
Keyword(s):  
Invertible Element ◽  
Multivalued Map ◽  
Algebraic Properties ◽  
Rings With Involution

We study several algebraic properties of dual covariance and weighted dual covariance sets in rings with involution andC*-algebras. Moreover, we show that the weighted dual covariance set, seen as a multivalued map, has some kind of continuity. Also, we prove weighed dual covariance set invariant under the bijection multiplicative*-functions.

Certain Submodules of Simple Rings with Involution, II

1975 ◽  
Vol 27 (3) ◽  
pp. 629-635 ◽  
Author(s):  
I. N. Herstein
Keyword(s):  
Simple Ring ◽  
Lie Ring ◽  
Jordan Ring ◽  
Rings With Involution ◽  
Image Position

Let R be a simple ring, of characteristic not 2, having an involution *. Let 5 = ﹛x G R|x* = x﹜ and K = ﹛x £ R|x* = — x﹜ be the set of symmetric and skew elements, respectively, of R.In [1] we discuss the structure of S as a Jordan ring and K as a Lie ring. In [2] we considered cross-over submodules, namely additive subgroups U ⊂ K, V ⊂ S such that

scholarly journals Structure of Hyperbolic Unitary Groups II: Classification of E-Normal Subgroups

2017 ◽  
Vol 24 (02) ◽  
pp. 195-232 ◽  
Author(s):  
Raimund Preusser
Keyword(s):  
Unitary Group ◽  
Direct Limit ◽  
Finite Ring ◽  
Unitary Groups ◽  
Normal Subgroups ◽  
Finite Rings ◽  
Elementary Subgroup ◽  
Rings With Involution ◽  
Hyperbolic Unitary Group

This paper proves the sandwich classification conjecture for subgroups of an even dimensional hyperbolic unitary group [Formula: see text] which are normalized by the elementary subgroup [Formula: see text], under the condition that R is a quasi-finite ring with involution, i.e., a direct limit of module finite rings with involution, and [Formula: see text].

On the Mathematical Basis of Zelen’s Prerandomized Designs

1985 ◽  
Vol 24 (03) ◽  
pp. 120-130 ◽  
Author(s):  
E. Brunner ◽  
N. Neumann
Keyword(s):  
Clinical Trial ◽  
Normal Distribution ◽  
Random Variables ◽  
Small Samples ◽  
Selection Effects ◽  
Sample Sizes ◽  
Mathematical Basis ◽  
Additional Assumptions

SummaryThe mathematical basis of Zelen’s suggestion [4] of pre randomizing patients in a clinical trial and then asking them for their consent is investigated. The first problem is to estimate the therapy and selection effects. In the simple prerandomized design (PRD) this is possible without any problems. Similar observations have been made by Anbar [1] and McHugh [3]. However, for the double PRD additional assumptions are needed in order to render therapy and selection effects estimable. The second problem is to determine the distribution of the statistics. It has to be taken into consideration that the sample sizes are random variables in the PRDs. This is why the distribution of the statistics can only be determined asymptotically, even under the assumption of normal distribution. The behaviour of the statistics for small samples is investigated by means of simulations, where the statistics considered in the present paper are compared with the statistics suggested by Ihm [2]. It turns out that the statistics suggested in [2] may lead to anticonservative decisions, whereas the “canonical statistics” suggested by Zelen [4] and considered in the present paper keep the level quite well or may lead to slightly conservative decisions, if there are considerable selection effects.

scholarly journals L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras

2019 ◽  
Vol 17 (1) ◽  
pp. 1538-1546
Author(s):  
Xin Zhou ◽  
Liangyun Chen ◽  
Yuan Chang
Keyword(s):  
Fuzzy Sets ◽  
Homomorphic Image ◽  
Quotient Algebra ◽  
Algebraic Properties ◽  
Novikov Algebras ◽  
Fuzzy Ideal

Abstract In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. We get a sufficient and neccessary condition such that an L-fuzzy subspace is an L-fuzzy ideal. Moreover, we show that the quotient algebra A/μ of the L-fuzzy ideal μ is isomorphic to the algebra A/Aμ of the non-fuzzy ideal Aμ. Finally, we discuss the algebraic properties of surjective homomorphic image and preimage of an L-fuzzy ideal.

On the Equilibrium Uniqueness in Cournot Competition with Demand Uncertainty

2020 ◽  
Vol 20 (2) ◽  
Author(s):  
Stefanos Leonardos ◽  
Costis Melolidakis
Keyword(s):  
Failure Rate ◽  
Demand Uncertainty ◽  
Sufficient Conditions ◽  
Cournot Competition ◽  
Uncertain Demand ◽  
Cournot Model ◽  
Equilibrium Uniqueness ◽  
Residual Demand ◽  
Uniqueness Of Equilibrium ◽  
Additional Assumptions

AbstractWe revisit the linear Cournot model with uncertain demand that is studied in Lagerlöf (2006. “Equilibrium Uniqueness in a Cournot Model with Demand Uncertainty.” The B.E. Journal of Theoretical Economics 6, no. 1. (Topics), Article 19: 1–6.) and provide sufficient conditions for equilibrium uniqueness that complement the existing results. We show that if the distribution of the demand intercept has the decreasing mean residual demand (DMRD) or the increasing generalized failure rate (IGFR) property, then uniqueness of equilibrium is guaranteed. The DMRD condition implies log-concavity of the expected profits per unit of output without additional assumptions on the existence or the shape of the density of the demand intercept and, hence, answers in the affirmative the conjecture of Lagerlöf (2006. “Equilibrium Uniqueness in a Cournot Model with Demand Uncertainty.” The B.E. Journal of Theoretical Economics 6, no. 1. (Topics), Article 19: 1–6.) that such conditions may not be necessary.

On Some Rings of Arithmetical Functions

1999 ◽  
Vol 6 (4) ◽  
pp. 299-306
Author(s):  
D. Bhattacharjee
Keyword(s):  
Arithmetical Functions ◽  
Algebraic Properties

Abstract In this paper we consider several constructions which from a given 𝐵-product *𝐵 lead to another one . We shall be interested in finding what algebraic properties of the ring 𝑅𝐵 = 〈𝐶ℕ, +, *𝐵〉 are shared also by the ring . In particular, for some constructions the rings 𝑅𝐵 and will be isomorphic and therefore have the same algebraic properties.

Sign in / Sign up

Export Citation Format

Share Document