Results 21 to 30 of about 11,627 (129)
Some Notes on Semiabelian Rings
International Journal of Mathematics and Mathematical Sciences, 2011 It is proved that if a ring R is semiabelian, then so is the skew polynomial ring R[x;σ], where σ is an endomorphism of R satisfying σ(e)=e for all e∈E(R). Some characterizations and properties of semiabelian rings are studied.
Junchao Wei, Nanjie Li
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Some homological properties of skew PBW extensions [PDF]
, 2013 We prove that if R is a left Noetherian and left regular ring then the same is true for any bijective skew PBW extension A of R. From this we get Serre's Theorem for such extensions.
Armando Reyes +2 more
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Derivations of skew polynomial rings
Publications de l'Institut Mathematique, 2002 Let \(R\) be a commutative ring of characteristic zero, \(d_1,d_2,\dots,d_n\) commuting derivations of \(R\), and \(A_n=R[X_1,X_2,\dots,X_n;d_1,d_2,\dots,d_n]\) a skew polynomial ring in commuting variables \(X_1,X_2,\dots,X_n\) over \(R\). The authors describe derivations of \(A_n\) and examine the lattice of its ideals, under certain conditions.
Hamaguchi, Naoki, Nakajima, Atsushi
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Derivations of Skew Polynomial Rings
Journal of Algebra, 1995 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Osborn, J.M., Passman, D.S.
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Skew Polynomial Rings: the Schreier Technique [PDF]
Acta Mathematica Vietnamica, 2022 AbstractSchreier bases are introduced and used to show that skew polynomial rings are free ideal rings, i.e., rings whose one-sided ideals are free of unique rank, as well as to compute a rank of one-sided ideals together with a description of corresponding bases. The latter fact, a so-called Schreier-Lewin formula (Lewin Trans. Am. Math.
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Some algebras similar to the 2x2 Jordanian matrix algebras
, 2016 The impetus for this study is the work of Dumas and Rigal on the Jordanian deformation of the ring of coordinate functions on $2\times 2$ matrices. We are also motivated by current interest in birational equivalence of noncommutative rings.
Gaddis, Jason, Price, Kenneth L.
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On the Notion of Complete Intersection outside the Setting of Skew Polynomial Rings
, 2015 In recent work of T. Cassidy and the author, a notion of complete intersection was defined for (non-commutative) regular skew polynomial rings, defining it using both algebraic and geometric tools, where the commutative definition is a special case.
Artin M. +5 more
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Indagationes Mathematicae (Proceedings), 1968 ABSTRACTSkew polynomial rings .are considered with a multiplication defined byx•a=a1x+a1x2+…+arxr,ai∈K,where K is a (skew) field and the ai depend on a ∈ K. Under certain conditions the rings appear to be non-commutative principal ideal rings with a unique factorization.
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Uniserial Rings and Skew Polynomial Rings
Tokyo Journal of Mathematics, 1984 If \(\tau\) is an automorphism of a division ring D then, for each positive integer c, the factor ring \(S/x^ cS\) of the skew polynomial ring \(S=D[x;\tau]\) is a local uniserial ring of split type. The purpose of this paper is to establish a necessary and sufficient condition on a local uniserial ring R for R to be isomorphic to a ring of the above ...
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Linear codes using skew polynomials with automorphisms and derivations
, 2014 International audienceIn this work the de nition of codes as modules over skew polynomial rings of automorphism type is generalized to skew polynomial rings whose multiplication is de ned using an automorphism and an inner derivation.
Boucher, Delphine, Ulmer, Félix
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