Results 11 to 20 of about 17,562 (171)
Frobenius Local Rings of Length 5 and Index of Nilpotency 3
MathematicsThis paper investigates finite local non-chain rings associated by the well-known invariants p,n,m,l, and k, where p is a prime number. In particular, we provide a comprehensive characterization of Frobenius local rings of length l=5 and index of ...
Sami Alabiad, Alhanouf Ali Alhomaidhi
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, 2022 In order to study graded Frobenius algebras from a ring theoretical perspective, we introduce graded quasi-Frobenius rings, graded Frobenius rings and a shift-version of the latter ones, and we investigate the structure and representations of such objects.
Dascalescu, Sorin +2 more
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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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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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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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$p$-adic Berglund-H\"ubsch Duality [PDF]
, 2014 Berglund-H\"ubsch duality is an example of mirror symmetry between orbifold Landau-Ginzburg models. In this paper we study a D-module-theoretic variant of Borisov's proof of Berglund-H\"ubsch duality.
Aldi, Marco, Peruničić, Andrija
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SQUARE-FREE DISCRIMINANTS OF FROBENIUS RINGS [PDF]
International Journal of Number Theory, 2010 Let E be an elliptic curve over ℚ. We know that the ring of endomorphisms of its reduction modulo an ordinary prime p is an order of the quadratic imaginary field generated by the Frobenius element πp. However, except in the trivial case of complex multiplication, very little is known about the fields that appear as algebras of endomorphisms when p ...
David, Chantal, Jiménez Urroz, Jorge
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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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Frobenius categories, Gorenstein algebras and rational surface singularities [PDF]
, 2014 We give sufficient conditions for a Frobenius category to be equivalent to the category of Gorenstein projective modules over an Iwanaga-Gorenstein ring.
Iyama, Osamu +3 more
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From Frobenius Structures to Differential Equations [PDF]
, 2008 Frobenius structures are omnipresent in arithmetic geometry. In this note we show that over suitable rings, Frobenius endomorphisms define differential structures and vice versa. This includes, for example, differential rings in positive characteristic
Matzat, B. Heinrich
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