Results 11 to 20 of about 1,334 (223)

Nilpotency in endomorphism rings [PDF]

Proceedings of the American Mathematical Society, 1974
Nil subrings of the endomorphism ring of a module with finite Krull dimension sequence are nilpotent. This includes the case of a module with finite Krull dimension as well as noetherian modules. The method used is to embed the endomorphism ring, modulo a nilpotent ideal, in the endomorphism ring of an artinian object of a Grothendieck category.
Robert Gordon
openaire   +3 more sources

Cogenerator endomorphism rings [PDF]

Proceedings of the American Mathematical Society, 1971
If R R is a ring and P P is a finitely generated projective right R R -module, what properties of R R does the R R -endomorphism ring of P P inherit? Rosenberg and Zelinsky have shown that if R R is quasi-Frobenius, and P
Ronald L. Wagoner
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Projectivity and flatness over the endomorphism ring of a finitely generated module [PDF]

International Journal of Mathematics and Mathematical Sciences, 2004
Let A be a ring and Λ a finitely generated A-module. We give necessary and sufficient conditions for projectivity and flatness of a module over the endomorphism ring of Λ.
S. Caenepeel, T. Guédénon
doaj   +2 more sources

H-module endomorphism rings [PDF]

Journal of Pure and Applied Algebra, 1995
Let \(H\) be a finite-dimensional Hopf algebra and \(A/B\) an \(H\)-Galois extension. Then for any right \(A\)-module \(M\) there is a ring isomorphism \(\text{End}_A(M\otimes_BA)\simeq\text{End}_B(M)\# H\). \(\text{End}_B(M)/\text{End}_A(M)\) is an \(H^*\)-extension. If moreover \(H\) is unimodular, \(\text{End}_B(M)/\text{End}_A(M)\) is Galois if and
Van Oystaeyen, F., Zhang, Y.
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The Supersingular Endomorphism Ring and One Endomorphism Problems are Equivalent [PDF]

, 2023
The supersingular Endomorphism Ring problem is the following: given a supersingular elliptic curve, compute all of its endomorphisms. The presumed hardness of this problem is foundational for isogeny-based cryptography. The One Endomorphism problem only asks to find a single non-scalar endomorphism.
Page, Aurel, Wesolowski, Benjamin
core   +8 more sources

Orienteering with One Endomorphism. [PDF]

Mathematica (N Y), 2023
In supersingular isogeny-based cryptography, the path-finding problem reduces to the endomorphism ring problem. Can path-finding be reduced to knowing just one endomorphism?
Arpin S, Chen M, Lauter KE, Scheidler R, Stange KE, Tran HTN.   +5 more
europepmc   +3 more sources

Orientations and the supersingular endomorphism ring problem [PDF]

, 2022
International audienceWe study two important families of problems in isogenybased cryptography and how they relate to each other: computing the endomorphism ring of supersingular elliptic curves, and inverting the action of class groups on oriented ...
Wesolowski, Benjamin, Benjamin Wesolowski   +1 more
core   +1 more source

Modules in which every surjective endomorphism has an e-small kernel

Journal of Kufa for Mathematics and Computer, 2023
In this paper we introduce the notion of e-gH modules which is a proper generalization of Hopfian modules and defined as, a module  is called e-gH if, any surjective -endomorphism  of  has an e-small kernel, a ring  is called e-gH if,  is e-gH. We
osama mohammed, Thaar Younis Ghawi
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Nilpotent graphs of skew polynomial rings over non-commutative rings [PDF]

Transactions on Combinatorics, 2020
Let $R$ be a ring and $\alpha$ be a ring endomorphism of $R$‎. ‎The undirected nilpotent graph of $R$‎, ‎denoted by $\Gamma_N(R)$‎, ‎is a graph with vertex set $Z_N(R)^*$‎, ‎and two distinct vertices $x$ and $y$ are connected by an edge if and only if ...
Mohammad Javad Nikmehr, Abdolreza Azadi
doaj   +1 more source

Rings whose additive endomorphisms are ring endomorphisms [PDF]

Bulletin of the Australian Mathematical Society, 1992
A ring R is said to be an AE-ring if every endomorphism of its additive group R+ is a ring endomorphism. Clearly, the zero ring on any abelian group is an AE-ring. In a recent article, Birkenmeier and Heatherly characterised the so-called standard AE-lings, that is, the non-trivial AE-rings whose maximal 2-subgroup is a direct summand.
Dugas, Manfred, Hausen, Jutta, Johnson, Johnny A.   +2 more
openaire   +1 more source