Rings of Morita contexts which are maximal orders

2016 ◽  
Vol 15 (07) ◽  
pp. 1650129 ◽  
Author(s):  
Bülent Saraç ◽  
Evrim Akalan ◽  
Pınar Aydoğdu ◽  
Hidetoshi Marubayashi
Keyword(s):  
Quotient Ring ◽  
Sufficient Conditions ◽  
Point Of View ◽  
Necessary And Sufficient Conditions ◽  
Maximal Order ◽  
Theoretical Point ◽  
Morita Context ◽  
Maximal Orders ◽  
Necessary And Sufficient

Let [Formula: see text] be a ring of Morita context which is a prime Goldie ring with its quotient ring [Formula: see text]. We define the notion of an [Formula: see text]-maximal module in [Formula: see text] and that of an [Formula: see text]-maximal module in [Formula: see text] from order theoretical point of view and give some necessary and sufficient conditions for [Formula: see text] to be a maximal order in terms of [Formula: see text]-module [Formula: see text] and [Formula: see text]-module [Formula: see text]. In case [Formula: see text] is a maximal order, we explicitly describe the structure of [Formula: see text]-[Formula: see text]-ideals. These results are applied to obtain necessary and sufficient conditions for [Formula: see text] to be an Asano order or a Dedekind order.

scholarly journals A Highly D‑efficient Spring Balance Weighing Design for an Even Number of Objects

2019 ◽  
Vol 5 (344) ◽  
pp. 17-27
Author(s):  
Małgorzata Graczyk ◽  
Bronisław Ceranka
Keyword(s):  
Optimal Design ◽  
Sufficient Conditions ◽  
Optimality Criteria ◽  
Point Of View ◽  
Necessary And Sufficient Conditions ◽  
Optimal Designs ◽  
Efficient Design ◽  
Spring Balance ◽  
Experimental Errors ◽  
Necessary And Sufficient

The problem of determining unknown measurements of objects in the model of spring balance weighing designs is presented. These designs are considered under the assumption that experimental errors are uncorrelated and that they have the same variances. The relations between the parameters of weighing designs are deliberated from the point of view of optimality criteria. In the paper, designs in which the product of the variances of estimators is possibly the smallest one, i.e. D‑optimal designs, are studied. A highly D‑efficient design in classes in which a D‑optimal design does not exist are determined. The necessary and sufficient conditions under which a highly efficient design exists and methods of its construction, along with relevant examples, are introduced.

Semicritical Rings and the Quotient Problem

1984 ◽  
Vol 27 (2) ◽  
pp. 160-170
Author(s):  
Karl A. Kosler
Keyword(s):  
Quotient Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Prime Ideals ◽  
Regular Elements ◽  
The Right ◽  
Minimal Prime ◽  
Necessary And Sufficient ◽  
Quotient Rings ◽  
The Relationship

AbstractThe purpose of this paper is to examine the relationship between the quotient problem for right noetherian nonsingular rings and the quotient problem for semicritical rings. It is shown that a right noetherian nonsingular ring R has an artinian classical quotient ring iff certain semicritical factor rings R/Ki, i = 1,…,n, possess artinian classical quotient rings and regular elements in R/Ki lift to regular elements of R for all i. If R is a two sided noetherian nonsingular ring, then the existence of an artinian classical quotient ring is equivalent to each R/Ki possessing an artinian classical quotient ring and the right Krull primes of R consisting of minimal prime ideals. If R is also weakly right ideal invariant, then the former condition is redundant. Necessary and sufficient conditions are found for a nonsingular semicritical ring to have an artinian classical quotient ring.

On the Ring of Quotients at a Prime Ideal of a Right Noetherian Ring

1972 ◽  
Vol 24 (4) ◽  
pp. 703-712 ◽  
Author(s):  
A. G. Heinicke
Keyword(s):  
Prime Ideal ◽  
Noetherian Ring ◽  
Quotient Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Torsion Class ◽  
Ring Of Quotients ◽  
Ore Condition ◽  
The Right ◽  
Necessary And Sufficient

J. Lambek and G. Michler [3] have initiated the study of a ring of quotients RP associated with a two-sided prime ideal P in a right noetherian ring R. The ring RP is the quotient ring (in the sense of [1]) associated with the hereditary torsion class τ consisting of all right R-modules M for which HomR(M, ER(R/P)) = 0, where ER(X) is the injective hull of the R-module X.In the present paper, we shall study further the properties of the ring RP. The main results are Theorems 4.3 and 4.6. Theorem 4.3 gives necessary and sufficient conditions for the torsion class associated with P to have property (T), as well as some properties of RP when these conditions are indeed satisfied, while Theorem 4.6 gives necessary and sufficient conditions for R to satisfy the right Ore condition with respect to (P).

Hilbert rings and G(oldman)-rings issued from amalgamated algebras

2018 ◽  
Vol 17 (02) ◽  
pp. 1850023 ◽  
Author(s):  
L. Izelgue ◽  
O. Ouzzaouit
Keyword(s):  
New York ◽  
Commutative Algebra ◽  
Quotient Ring ◽  
Sufficient Conditions ◽  
Ring Homomorphism ◽  
Necessary And Sufficient Conditions ◽  
Local Rings ◽  
Finitely Generated ◽  
Necessary And Sufficient ◽  
The Way

Let [Formula: see text] and [Formula: see text] be two rings, [Formula: see text] an ideal of [Formula: see text] and [Formula: see text] be a ring homomorphism. The ring [Formula: see text] is called the amalgamation of [Formula: see text] with [Formula: see text] along [Formula: see text] with respect to [Formula: see text]. It was proposed by D’anna and Fontana [Amalgamated algebras along an ideal, Commutative Algebra and Applications (W. de Gruyter Publisher, Berlin, 2009), pp. 155–172], as an extension for the Nagata’s idealization, which was originally introduced in [Nagata, Local Rings (Interscience, New York, 1962)]. In this paper, we establish necessary and sufficient conditions under which [Formula: see text], and some related constructions, is either a Hilbert ring, a [Formula: see text]-domain or a [Formula: see text]-ring in the sense of Adams [Rings with a finitely generated total quotient ring, Canad. Math. Bull. 17(1) (1974)]. By the way, we investigate the transfer of the [Formula: see text]-property among pairs of domains sharing an ideal. Our results provide original illustrating examples.

scholarly journals On uniform exponential trisplitting for cocycles of linear operators in Banach spaces

2018 ◽  
Vol 56 (2) ◽  
pp. 81-103
Author(s):  
Larisa Elena Biriş ◽  
Claudia Luminiţa Mihiţ ◽  
Traian Ceauşu ◽  
Ioan-Lucian Popa
Keyword(s):  
Banach Spaces ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Type A ◽  
Point Of View ◽  
Necessary And Sufficient Conditions ◽  
Linear Operators ◽  
Skew Product ◽  
Exponential Trichotomy ◽  
Necessary And Sufficient

AbstractThe aim of this paper is to study the concept of uniform exponential trisplitting for skew-product semiflow in Banach spaces. This concept is a generalisation of the well-known concept of uniform exponential trichotomy. We obtain necessary and sufficient conditions for this concept of Datko’s type. a character-isation in terms of Lyapunov functions is provided. The results are obtained from the point of view of the projector families, i.e. invariant and strongly invariant.

scholarly journals Necessary and sufficient conditions for unitary similarity

1961 ◽  
Vol 2 (1) ◽  
pp. 122-126 ◽  
Author(s):  
N. A. Wiegmann
Keyword(s):  
Representation Theory ◽  
Canonical Form ◽  
Group Representation ◽  
Sufficient Conditions ◽  
Point Of View ◽  
Necessary And Sufficient Conditions ◽  
Unitary Matrix ◽  
Unitary Similarity ◽  
Conjugate Transpose ◽  
Necessary And Sufficient

If A and B are two complex matrices and if U is a complex unitary matrix such that UAUCT = B (where UCT denotes the conjugate transpose of U), then A and B are said to be unitarily similar. Necessary and sufficient conditions that two matrices be unitarily similar have been dealt with in [5] (from the point of view of group representation theory) and in [2] (from the point of view of developing a canonical form under unitary similarity).

SIFAT-SIFAT RING FAKTOR YANG DILENGKAPI DERIVASI

2018 ◽  
Vol 1 (1) ◽  
pp. 12
Author(s):  
Iwan Ernanto
Keyword(s):  
Quotient Ring ◽  
Sufficient Conditions ◽  
Unit Element ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

Let $R$ is a ring with unit element and $\delta$ is a derivation on $R$. An ideal $I$ of $R$ is called $\delta$-ideal if it satisfies $\delta (I)\subseteq I$. Related to the theory of ideal, we can define prime $\delta$-ideal and maximal $\delta$-ideal. The ring $R$ is called $\delta$-simple if $R$ is non-zero and the only $\delta$-ideal of $R$ are ${0}$ and $R$. In this paper, given the necessary and sufficient conditions for quotient ring $R/I$ is a $\delta$-simple where $\delta_*$ is a derivation on $R/I$ such that $\delta_* \circ \pi =\pi \circ \delta$.

On the Necessary and Sufficient Conditions for Homokinetic Transmission in Chains of Cardan Joints

1993 ◽  
Vol 115 (2) ◽  
pp. 255-261 ◽  
Author(s):  
D. A. Johnson ◽  
P. Y. Willems
Keyword(s):  
Constant Velocity ◽  
Velocity Ratio ◽  
Sufficient Conditions ◽  
Point Of View ◽  
Necessary And Sufficient Conditions ◽  
Flexible Design ◽  
Universal Joint ◽  
Necessary And Sufficient ◽  
Ratio Transmission

The classical double universal joint for constant velocity ratio transmission is subject to strict geometrical requirements as regards configuration, and it is generally accepted that similar constraints also prevail for longer chains of joints. This paper examines the constant velocity conditions from a necessary point of view and establishes new configuration possibilities for chains of 3 or more joints, which allow to envisage more flexible design in some applications.

scholarly journals Skew group rings and maximal orders

1995 ◽  
Vol 37 (2) ◽  
pp. 249-263 ◽  
Author(s):  
R. Martin
Keyword(s):  
Finite Group ◽  
Noetherian Ring ◽  
Sufficient Conditions ◽  
Maximal Order ◽  
Group Rings ◽  
Maximal Orders ◽  
Noetherian Domain ◽  
A Finite Group ◽  
Necessary And Sufficient ◽  
Skew Group Ring

Let S be a prime Noetherian ring and G a finite group acting on 5 such that Gis x-outer on S. We give sufficient conditions for the skew group ring S * Gto be a prime maximal order. If we impose the further hypothesis that the order of Gbe a unit of S, then these conditions are also necessary. Moreover, if S is a commutative Noetherian domain, then there are necessary and sufficient conditions for S*Gto be a prime maximal order, without requiring that the order of G be a unit in S.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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