Results 11 to 20 of about 4,472,960 (363)
Enveloping algebras that are principal ideal rings [PDF]
Journal of Pure and Applied Algebra, 2017 Let $L$ be a restricted Lie algebra over a field of positive characteristic. We prove that the restricted enveloping algebra of $L$ is a principal ideal ring if and only if $L$ is an extension of a finite-dimensional torus by a cyclic restricted Lie algebra.
SICILIANO, Salvatore, Usefi, Hamid
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Morphic and principal-ideal group rings [PDF]
Journal of Algebra, 2007 We observe that the class of left and right artinian left and right morphic rings agrees with the class of artinian principal ideal rings. For $R$ an artinian principal ideal ring and $G$ a group, we characterize when $RG$ is a principal ideal ring; for finite groups $G$, this characterizes when $RG$ is a left and right morphic ring.
Chen +16 more
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A generalization of the principal ideal theorem [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1949 Tadao Tannaka, Fumiyuki Terada
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Null ideals of matrices over residue class rings of principal ideal domains [PDF]
, 2015 Given a square matrix $A$ with entries in a commutative ring $S$, the ideal of $S[X]$ consisting of polynomials $f$ with $f(A) =0$ is called the null ideal of $A$. Very little is known about null ideals of matrices over general commutative rings.
Roswitha Rissner
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On the rank decoding problem over finite principal ideal rings [PDF]
International Journal of Applied Mathematics and Computer Sciences, 2021 The rank decoding problem has been the subject of much attention in this last decade. This problem, which is at the base of the security of public-key cryptosystems based on rank metric codes, is traditionally studied over finite fields.
Hervé Talé Kalachi +1 more
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On representations of general linear groups over principal ideal local rings of length two [PDF]
, 2010 We study the irreducible complex representations of general linear groups over principal ideal local rings of length two with a fixed finite residue field. We construct a canonical correspondence between the irreducible representations of all such groups
Pooja Singla
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On the general principal ideal theorem [PDF]
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1980 Katsuya Miyake
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Characterization of irreducible polynomials over a special principal ideal ring [PDF]
Mathematica Bohemica, 2023 A commutative ring $R$ with unity is called a special principal ideal ring (SPIR) if it is a non integral principal ideal ring containing only one nonzero prime ideal, its length $e$ is the index of nilpotency of its maximal ideal. In this paper, we show
Brahim Boudine
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On the level of principal ideal domains
Archiv der Mathematik, 2011 We construct principal ideal domains with level different from the level of their fields of fractions. We also make some remarks on the sublevel of principal ideal domains.
Arason, J.K., Baeza, R.
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MacWilliams' Extension Theorem for bi-invariant weights over finite principal ideal rings [PDF]
Journal of Combinatorial Theory, 2013 A finite ring R and a weight w on R satisfy the Extension Property if every R-linear w-isometry between two R-linear codes in R^n extends to a monomial transformation of R^n that preserves w.
M. Greferath +4 more
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