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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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Formal Groups and Hopf Algebras over Discrete Rings [PDF]
, 1974 A theory of formal schemes and groups over abitrary rings is presented. The flat formal schemes in this theory have coalgebras of distributions which behave in the usual way. Frobenius and Verschiebung maps are studied.
Robert A. Morris +3 more
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MacWilliams extending conditions and quasi-Frobenius rings [PDF]
, 2022 © 2022 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This document is the Accepted Manuscript version of a Published Work that appeared in final form in ...
Srivastava, Ashish K. +1 more
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Exponent matrices and Frobenius rings [PDF]
, 2014 We give a survey of results connecting the exponent matrices with Frobenius rings. In particular, we prove that for any parmutation σ ∈ Sn there exists a countable set of indecomposable Frobenius semidistributive rings Am with Nakayama permutation σ.The ...
Kirichenko, V.V. +3 more
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Cyclic codes over local Frobenius rings of order 16
Advances in Mathematics of Communications, 2017 We study cyclic codes over commutative local Frobenius rings of order 16 and give their binary images under a Gray map which is a generalization of the Gray maps on the rings of order 4.
S. Dougherty, A. Kaya, Esengül Saltürk
semanticscholar +1 more source
, 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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A Remark on Frobenius Extensions and Endomorphism Rings [PDF]
Nagoya Mathematical Journal, 1959 In his paper [1] F. Kasch developed a theory of Frobenius extensions as a generalization of the theory of Frobenius algebras. In it he established a very interesting relationship between the Frobenius property of an extension and that of its endomorphism ring [1, Satz 5], from which he further derived the Frobenius extension property of Galois ...
Nakayama, Tadasi, Tsuzuku, Tosiro
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Remarks on quasi-Frobenius rings
Illinois Journal of Mathematics, 1958 J. Dieudonne
semanticscholar +4 more sources
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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Kloosterman sums over finite Frobenius rings [PDF]
, 2021 We study Kloosterman sums in a generalized ring-theoretic context, that of finite commutative Frobenius rings. We prove a number of identities for twisted Kloosterman sums, loosely clustered around moment computations.
Nica, Bogdan
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