On the Yoneda Ext-Algebras of Semiperfect Algebras

2008 ◽  
Vol 15 (02) ◽  
pp. 207-222 ◽  
Author(s):  
Jiwei He ◽  
Yu Ye
Keyword(s):  
Jacobson Radical ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Yoneda Algebra ◽  
Ideal Formula ◽  
Morita Equivalent ◽  
Morita Invariant ◽  
The Right ◽  
Necessary And Sufficient

It is proved that the Yoneda Ext-algebras of Morita equivalent semiperfect algebras are graded equivalent. The Yoneda Ext-algebras of noetherian semiperfect algebras are studied in detail. Let A be a noetherian semiperfect algebra with Jacobson radical J. We construct a right ideal [Formula: see text] of the Yoneda algebra [Formula: see text], which plays an important role in the discussion of the structure of E(A). An extra grading is introduced to [Formula: see text], by which we give a description of the right ideal of E(A) generated by [Formula: see text], and we give a necessary and sufficient condition for a notherian semiperfect algebra to be higher quasi-Koszul. Finally, it is shown that the quasi-Koszulity of a noetherian semiperfect algebra is a Morita invariant.

Comaximal factorization of lifting ideals

2020 ◽  
pp. 2250044
Author(s):  
Esmaeil Rostami ◽  
Sina Hedayat ◽  
Reza Nekooei ◽  
Somayeh Karimzadeh
Keyword(s):  
Commutative Ring ◽  
Proper Ideal ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
New Approach ◽  
Ideal Formula ◽  
Basic Properties ◽  
Necessary And Sufficient

A proper ideal [Formula: see text] of a commutative ring [Formula: see text] is called lifting whenever idempotents of [Formula: see text] lift to idempotents of [Formula: see text]. In this paper, many of the basic properties of lifting ideals are studied and we prove and extend some well-known results concerning lifting ideals and lifting idempotents by a new approach. Furthermore, we give a necessary and sufficient condition for every proper ideal of a commutative ring to be a product of pairwise comaximal lifting ideals.

Russian ‘Liberal’ Opposition: The Divide Be-Tween ‘Radicals’ and ‘Moderates’?

2013 ◽  
Vol 9 (1) ◽  
pp. 63-70
Author(s):  
Anna Taitslin
Keyword(s):  
Rule Of Law ◽  
Private Property ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Social Consensus ◽  
The Rule Of Law ◽  
The One ◽  
The Right ◽  
Necessary And Sufficient ◽  
Party State

The paper reflects on the divide emerged amidst the liberal opposition in Russia between the left liberals and the right liberals. The divide is not just about split-up between the radicals and the moderates. It re-flects the crisis of liberal ideas as formed in the 1990s, when the tran-sition to economy based on private property was seen as necessary and sufficient condition for dismantling the command economy and the one-party state. The ultimate issue at hand is the notion of the rule of law and a possibility of wider social consensus on the minimal rule of law threshold.

scholarly journals Fuzzy Small Submodule and Jacobson -Radical

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Saifur Rahman ◽  
Helen K. Saikia
Keyword(s):  
Jacobson Radical ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Direct Sum ◽  
Necessary And Sufficient ◽  
Quotient Modules ◽  
Small Submodule

Using the notion of fuzzy small submodules of a module, we introduce the concept of fuzzy coessential extension of a fuzzy submodule of a module. We attempt to investigate various properties of fuzzy small submodules of a module. A necessary and sufficient condition for fuzzy small submodules is established. We investigate the nature of fuzzy small submodules of a module under fuzzy direct sum. Fuzzy small submodules of a module are characterized in terms of fuzzy quotient modules. This characterization gives rise to some results on fuzzy coessential extensions. Finally, a relation between small -submodules and Jacobson -radical is established.

scholarly journals On right self-injective regular semigroups, II

1983 ◽  
Vol 34 (2) ◽  
pp. 182-198 ◽  
Author(s):  
Kunitaka Shoji
Keyword(s):  
Extension Property ◽  
Sufficient Condition ◽  
Congruence Extension Property ◽  
Necessary And Sufficient Condition ◽  
Regular Semigroups ◽  
Left Congruence ◽  
Spined Product ◽  
The Right ◽  
Necessary And Sufficient

AbstractIt is shown that a semigroup is right self-injective and a band of groups if and only if it is isomorphic to the spined product of a self-injective semilattice of groups and a right self-injective band. A necessary and sufficient condition for a band to be right self-injective is given. It is shown that a left [right] self-injective semigroup has the [anti-] representation extension property and the right [left] congruence extension property.

scholarly journals On Approximation of the Perturbed Inclusion

2007 ◽  
Vol 14 (2) ◽  
pp. 253-267
Author(s):  
Alexander I. Bulgakov ◽  
Anna A. Grigorenko ◽  
Anatoliy I. Korobko
Keyword(s):  
Stable Process ◽  
Approximate Solutions ◽  
Continuous Functions ◽  
The Other ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Space Of Continuous Functions ◽  
Linear Integral ◽  
The Right ◽  
Necessary And Sufficient

Abstract The paper is concerned with the so-called perturbed inclusion in the space of continuous functions. The right-hand side of the inclusion is represented by an algebraic sum of the values of two multi-valued maps, one of which consists of compacts and the other is not necessarily closed-valued and is a composition of a linear integral operator and multimap convex-valued with respect to switching. For such an inclusion it is proved that approximation in the space of summable functions of the values of a multimap convex-valued with respect to switching is not always a stable process. The necessary and sufficient condition for the closure of the set of approximate solutions to converge to the closure of the set of solutions for perturbed inclusion is derived.

scholarly journals Multivaluedness in Networks: Theory

2020 ◽  
Author(s):  
Anton van Wyk
Keyword(s):  
Structural Complexity ◽  
The Other ◽  
Sufficient Condition ◽  
The Novel ◽  
Necessary And Sufficient Condition ◽  
Cascaded Systems ◽  
The Right ◽  
Necessary And Sufficient ◽  
Theoretical Results

<div>An unexpected and somewhat surprising observation is that two counter-cascaded systems,12 satisfying the right conditions, implicitly exhibit multivaluedness from one of the outputs to the other. Based on the novel notions of immanence and transcendence, the main result presented here, gives a necessary and sufficient condition for multivaluedness to be exhibited by counter-cascaded systems. Subsequent corollaries provide further characterization of multivaluedness under specific conditions.</div><div><br></div><div>As an application of these theoretical results, we demonstrate how these aid in the structural complexity reduction of directed complex networks.</div>

scholarly journals A necessary and sufficient condition for the existence of a mobile singular points for a third-order nonlinear differential equation

2021 ◽  
pp. 49-55
Author(s):  
Темирхан Султанович Алероев ◽  
Магомедюсуф Владимирович Гасанов
Keyword(s):  
Differential Equation ◽  
Nonlinear Differential Equation ◽  
Order Equation ◽  
Singular Points ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Degree Polynomial ◽  
Third Order ◽  
The Right ◽  
Necessary And Sufficient

Рассматривается нелинейное уравнение третьего порядка с полиномом второй степени в правой части. Отличительной чертой этого класса уравнений является наличие подвижных особенностей, что делает эти уравнения неразрешимыми в квадратурах. В работе получены интервальные критерии существование подвижных особых точек. Представленная теория является подспорьем для написания различных алгоритмов в различных программных комплексах для нахождения подвижных особых точек. A nonlinear third-order equation with second degree polynomial on the right. The hallmark of this class equations is the presence of movable singularities, which makes these equations undecidable in quadratures. The work obtained interval criteria the existence of movable singular points. The theory presented is help for writing various algorithms in various software complexes for finding movable singular points.

scholarly journals Topological mixing of Weyl chamber flows

2020 ◽  
pp. 1-27
Author(s):  
NGUYEN-THI DANG ◽  
OLIVIER GLORIEUX
Keyword(s):  
Weyl Chamber ◽  
Sufficient Condition ◽  
Topological Properties ◽  
Necessary And Sufficient Condition ◽  
Right Action ◽  
Topological Mixing ◽  
The Right ◽  
Necessary And Sufficient

In this paper we study topological properties of the right action by translation of the Weyl chamber flow on the space of Weyl chambers. We obtain a necessary and sufficient condition for topological mixing.

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