Results 11 to 20 of about 17,639 (169)
Frobenius and valuation rings [PDF]
Algebra & Number Theory, 2016 The behavior of the Frobenius map is investigated for valuation rings of prime characteristic. We show that valuation rings are always F-pure. We introduce a generalization of the notion of strong F-regularity, which we call F-pure regularity, and show that a valuation ring is F-pure regular if and only if it is Noetherian.
Datta, Rankeya, Smith, Karen
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Rings of Frobenius operators [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2014 AbstractLet R be a local ring of prime characteristic. We study the ring of Frobenius operators ${\mathcal F}(E)$, where E is the injective hull of the residue field of R. In particular, we examine the finite generation of ${\mathcal F}(E)$ over its degree zero component ${\mathcal F}^0(E)$, and show that ${\mathcal F}(E)$ need not be finitely ...
Katzman, Mordechai +3 more
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On Almost Quasi-Frobenius Fuzzy Rings
مجلة بغداد للعلوم, 2004 In this paper, we introduce the concept of almost Quasi-Frobcnius fuzzy ring as a " " of Quasi-Frobenius ring. We give some properties about this concept with qoutient fuzzy ring. Also, we study the fuzzy external direct sum of fuzzy rings.
Baghdad Science Journal
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On the Weight Distribution of Codes over Finite Rings [PDF]
, 2011 Let R > S be finite Frobenius rings for which there exists a trace map T from R onto S as left S modules. Let C:= {x -> T(ax + bf(x)) : a,b in R}. Then C is an S-linear subring-subcode of a left linear code over R.
Byrne, Eimear
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A Generalization of Quasi-Frobenius Rings [PDF]
Proceedings of the American Mathematical Society, 1969 Let \(R\) be a ring and \(_R\mathcal M\) the category of all left \(R\)-modules. \textit{G. Azumaya} [Nagoya Math. J. 27, 697--708 (1966; Zbl 0144.02303)] proved that if all faithful left \(R\)-modules are generators in \(_R\mathcal M\), \(R\) is left self-injective and a direct sum of indecomposable left ideals having minimal left ideals (cf.
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On the (non)rigidity of the Frobenius Endomorphism over Gorenstein Rings [PDF]
, 2010 It is well-known that for a large class of local rings of positive characteristic, including complete intersection rings, the Frobenius endomorphism can be used as a test for finite projective dimension.
Dao, H., Li, J., Miller, C.
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Witt Vector Rings and the Relative de Rham Witt Complex [PDF]
, 2015 In this paper we develop a novel approach to Witt vector rings and to the (relative) de Rham Witt complex. We do this in the generality of arbitrary commutative algebras and arbitrary truncation sets.
Cuntz, Joachim, Deninger, Christopher
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FTF Rings and Frobenius Extensions
Journal of Algebra, 2002 Let \(R\) be a ring with identity element. Then \(R\) is called a left FTF ring if there exists a hereditary torsion theory \(\gamma\) on \(R\)-mod such that a left \(R\)-module \(M\) is \(\gamma\)-torsionfree if and only if \(M\) embeds in a flat left \(R\)-module. Let \(\lambda\) denote the Lambek torsion theory.
Gómez-Torrecillas, J., Torrecillas, B.
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The Frobenius Structure of Local Cohomology [PDF]
, 2008 Given a local ring of positive prime characteristic there is a natural Frobenius action on its local cohomology modules with support at its maximal ideal.
Enescu, Florian, Hochster, Melvin
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A note on quasi-Frobenius rings [PDF]
Pacific Journal of Mathematics, 1968 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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