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ON RADICAL FORMULA IN MODULES

Published online by Cambridge University Press:  01 August 2011

A. NIKSERESHT  and
A. AZIZI
A. NIKSERESHT
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, Shiraz, 71457-44776, Iran e-mails: [email protected], [email protected]
A. AZIZI
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, Shiraz, 71457-44776, Iran e-mails: [email protected], [email protected]
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Abstract

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We will state some conditions under which if a quotient of a module M satisfies the radical formula of degree k (s.t.r.f of degree k), so does M. Especially, we will introduce some particular modules M′ such that M′ ⊕ M″ s.t.r.f of degree k, when M″ s.t.r.f of degree k. Furthermore, we will show that, under certain conditions, if the completion of a module M s.t.r.f of degree k, then there is a non-negative integer k′ such that M s.t.r.f. of degree k′. Moreover, we state a corrected version of Leung and Man's theorem (K. H. Leung and S. H. Man, On commutative Noetherian rings which satisfy the radical formula, Glasgow Math. J. 39 (1997), 285–293) on Noetherian rings that satisfies the radical formula.

Keywords

13C9913A1513C13
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 3 , September 2011 , pp. 657 - 668
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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