Basic Module Theory over Non-commutative Rings with Computational Aspects of Operator Algebras

DOI10.1007/978-3-642-54479-8_2zbMath1375.16001arXiv1312.7096OpenAlexW1583847540MaRDI QIDQ5403089

José Gómez-Torrecillas

Publication date: 25 March 2014

Published in: Algebraic and Algorithmic Aspects of Differential and Integral Operators (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.7096

zbMATH Keywords

Gröbner basisfree resolutionGelfand-Kirillov dimensionfinitely presented moduleOre extensionJacobson normal formnon-commutative factorizationfiltered ringnon-commutative ringPBW algebraeigenringgrade numberPBW ring

Mathematics Subject Classification ID

Ordinary and skew polynomial rings and semigroup rings (16S36) Research exposition (monographs, survey articles) pertaining to operator theory (47-02) Computational aspects of associative rings (general theory) (16Z05) Research exposition (monographs, survey articles) pertaining to associative rings and algebras (16-02)

Related Items (12)

Algebraic Theory of Linear Systems: A Survey ⋮ An isomorphism test for modules over a non-commutative PID. Applications to similarity of Ore polynomials. ⋮ How to obtain lattices from \((f,\sigma,\delta)\)-codes via a generalization of construction A ⋮ Finite nonassociative algebras obtained from skew polynomials and possible applications to \((f,\sigma,\delta)\)-codes ⋮ Algorithmic operator algebras via normal forms in tensor rings ⋮ On noncommutative finite factorization domains ⋮ HOW A NONASSOCIATIVE ALGEBRA REFLECTS THE PROPERTIES OF A SKEW POLYNOMIAL ⋮ The automorphisms of Petit’s algebras ⋮ Algebras whose right nucleus is a central simple algebra ⋮ Computing the bound of an Ore polynomial. Applications to factorization ⋮ Normal Forms for Operators via Gröbner Bases in Tensor Algebras ⋮ Dual skew codes from annihilators: Transpose Hamming ring extensions

Uses Software

• OreMorphisms
• NCPOLY

Cites Work

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