A counter example to a conjecture of Johns

Faith, Carl; Menal, Pere

doi:10.1090/s0002-9939-1992-1100651-0

Cited by 32 publications

(17 citation statements)

References 11 publications

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“…Several properties of right Johns rings were highlighted in [8] and a number of necessary and sufficient conditions for a strongly right Johns ring to be QF were collected in [9]. In the next proposition we deduce several new properties of these rings.…”

Section: Johns Ringsmentioning

confidence: 83%

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Annihilators and the CS-condition

Nicholson

Yousif

1998

Glasgow Math. J.

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Abstract. It is proved that if every cyclic right /^-module is torsionless and R is a left CS-ring then R is semiperfect left continuous with soc(R R ) essential in R R. As a consequence every right cogenerator, left CS-ring R is shown to be right pseudo-Frobenius and left continuous, and an example is given to show that R need not be left selfinjective. It is also proved that if R is a left CS-ring and every cyclic right /^-module embeds in a free module, then R is quasi-Frobenius if and only if J(R) c Z(R R ). Introduction.Right CS-rings with certain cogenerating (annihilator) conditions were considered by Gomez-Pardo and Guil Asensio in [10] and [11]. For example they show that if R is a right CS-ring and every cyclic (finitely generated) right 7?-module embeds in a free module then R is right artinian (quasi-Frobenius). They also prove that if R is a right cogenerator right CS-ring then R is right pseudo-Frobenius.In this paper we consider these same classes of rings but with the left CS-condition rather than the right CS-condition. We show that if R is a left CS-ring and every cyclic right /^-module is torsionless, then R is a semiperfect left continuous ring with SOC(RR) C.

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Section: Johns Ringsmentioning

confidence: 83%

“…According to Menal and Faith [8] a ring R is called right Johns if R is a right noetherian ring in which every right ideal is an annihilator. In [9] R is called strongly right Johns if every n x n matrix ring M n (R) is right Johns.…”

Section: Johns Ringsmentioning

confidence: 99%

Annihilators and the CS-condition

Nicholson

Yousif

1998

Glasgow Math. J.

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“…In general, a right Noetherian ring with essential right socle need not be right Artinian as shown by Faith-Menal's example ( [7]). The following theorem shows that the condition S r c 5/ is strong enough to force a right Noetherian ring with essential right socle to be right Artinian.…”

Section: A Ringmentioning

confidence: 99%

“…This is not true for arbitrary right Noetherian rings ( [7,8]). However a result of Ginn and Moss [8,Theorem] asserts that a two-sided Noetherian ring with essential right socle is right and left Artinian.…”

Section: Introductionmentioning

confidence: 99%

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On Noetherian rings with essential socle

Chen¹,

Ding²,

Yousif³

2004

J. Aust. Math. Soc.

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It is shown that if R is a right Noetherian ring whose right socle is essential as a right ideal and is contained in the left socle, then R is right Artinian. This result may be viewed as a one-sided version of a result of Ginn and Moss on two-sided Noetherian rings with essential socle. This also extends the work of Nicholson and Yousif where the same result is obtained under a stronger hypothesis. We use our work to obtain partial positive answers to some open questions on right CF, right FGF and right Johns rings.2000 Mathematics subject classification: primary 16A33; secondary 16A35.

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Derivatives of Faber Polynomials and Markov Inequalities

Pritsker

2002

Journal of Approximation Theory

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We study asymptotic behavior of the derivatives of Faber polynomials on a set with corners at the boundary. Our results have applications to the questions of sharpness of Markov inequalities for such sets. In particular, the found asymptotics are related to a general Markov-type inequality of Pommerenke and the associated conjecture of Erd + o os. We also prove a new bound for Faber polynomials on piecewise smooth domains. # 2002 Elsevier Science (USA)

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A counter example to a conjecture of Johns

Cited by 32 publications

References 11 publications

Annihilators and the CS-condition

Annihilators and the CS-condition

On Noetherian rings with essential socle

Derivatives of Faber Polynomials and Markov Inequalities

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