COMPUTING NILPOTENT QUOTIENTS OF ASSOCIATIVE ALGEBRAS AND ALGEBRAS SATISFYING A POLYNOMIAL IDENTITY

DOI10.1142/S0218196711006649zbMath1239.16026OpenAlexW2027459617MaRDI QIDQ3110890

Bettina Eick

Publication date: 16 January 2012

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218196711006649

zbMATH Keywords

nil algebrasPI-algebrasrelatively free algebrasnilpotent quotient algorithmfinitely presented associative algebras

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Finite rings and finite-dimensional associative algebras (16P10) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Nil and nilpotent radicals, sets, ideals, associative rings (16N40) Computational aspects of associative rings (general theory) (16Z05) (T)-ideals, identities, varieties of associative rings and algebras (16R10)

Related Items (5)

On automorphisms of groups, rings, and algebras ⋮ ASSOCIATIVE NIL-ALGEBRAS OVER FINITE FIELDS ⋮ The isomorphism problem for graded algebras and its application to \(\mathrm{mod-}p\) cohomology rings of small \(p\)-groups. ⋮ Coclass Theory for Finite Nilpotent Associative Algebras: Algorithms and a Periodicity Conjecture ⋮ A nilpotent quotient algorithm for finitely presented associative ℤ-algebras and its application to integral group rings

Uses Software

• GAP

Cites Work

• Unnamed Item
• A nilpotent quotient algorithm for graded Lie rings
• Computing automorphism groups and testing isomorphisms for modular group algebras.
• An algorithm for computing graded algebras
• Bounds for indices of nilpotency and nility
• APPLICATION OF COMPUTERS TO QUESTIONS LIKE THOSE OF BURNSIDE, II
• SOME OPEN PROBLEMS IN THE THEORY OF INFINITE DIMENSIONAL ALGEBRAS
• Relatively Free Algebras with the Identityx³ = 0^#
• On a problem of Kurosch and Jacobson

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