Free products of units in algebras. I: Quaternion algebras

DOI10.1006/jabr.1998.7680zbMath0934.16026OpenAlexW2030743146MaRDI QIDQ1283277

Arnaldo Mandel, Mazi Shirvani, Jairo Z. Goncalves

Publication date: 27 January 2000

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1998.7680

zbMATH Keywords

skew polynomial ringsfree productsquaternion algebrasgroups of unitsfree groupsfree pairs of elementsMalcev-Neumann skewfieldssemifree pairs

Mathematics Subject Classification ID

Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) (16S10) Subgroup theorems; subgroup growth (20E07) Ordinary and skew polynomial rings and semigroup rings (16S36) Valuations, completions, formal power series and related constructions (associative rings and algebras) (16W60) Free nonabelian groups (20E05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Finite-dimensional division rings (16K20) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Units, groups of units (associative rings and algebras) (16U60)

Related Items (18)

Unnamed Item ⋮ A Survey on Free Objects in Division Rings and in Division Rings with an Involution ⋮ An exotic group as limit of finite special linear groups ⋮ Free symmetric and unitary pairs in division rings infinite-dimensional over their centers. ⋮ Free symmetric and unitary pairs in the field of fractions of torsion-free nilpotent group algebras ⋮ Free unit groups in group rings and division rings: My collaboration with Don Passman ⋮ Free symmetric pairs in the field of fractions of enveloping Lie algebras with involution ⋮ Free Groups in Central Simple Algebras without Tits' Theorem ⋮ Free pairs of symmetric and unitary units in normal subgroups of a division ring ⋮ A SURVEY ON FREE SUBGROUPS IN THE GROUP OF UNITS OF GROUP RINGS ⋮ FREE SYMMETRIC AND UNITARY PAIRS IN DIVISION RINGS WITH INVOLUTION ⋮ Free Subgroups in the Units of ℤ[K₈ × C_p] ⋮ Free groups in normal subgroups of the multiplicative group of a division ring. ⋮ Free pairs of symmetric elements in normal subgroups of division rings ⋮ On free subgroups in division rings ⋮ A NON-COMMUTATIVITY STATEMENT FOR ALGEBRAIC QUATERNIONS ⋮ Explicit free groups in division rings ⋮ Free products of units in algebras. II: Crossed products

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On group rings of nilpotent groups
• Are there free groups in division rings?
• On subnormal subgroups of skew fields
• Free group algebras in certain division rings
• On normal subgroups of multiplicative group of skew fields generated by a polycyclic-by-finite group
• Free group algebras in the field of fractions of differential polynomial rings and enveloping algebras
• A class of free rotation groups
• Valuation methods in division rings
• Free subgroups in linear groups
• Orthogonal Isomorphic Representations Of Free Groups
• On Free Products of Cyclic Rotation Groups
• Free Groups in Subnormal Subgroups and the Residual Nilpotence of the Group of Units of Groups Rings
• Free Subgroups in the Unit Groups of Integral Group Rings
• On Subgroups of the Multiplicative Group of Skew Fields
• Free Subgroups of Normal Subgroups of the Multiplicative Group of Skew Fields
• On Embedding of Group Rings of Residually Torsion Free Nilpotent Groups into Skew Fields
• On faithful representations of free products of groups

This page was built for publication: Free products of units in algebras. I: Quaternion algebras