Abstract
We prove the isomorphism problem for integral loop rings of finitely generated RA loops using a decomposition of the loop of units. Also we describe the finitely generated RA loops whose loops of units satisfy a certain property.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L.G.X. de Barros and S.O. Juriaans, Units in Integral Loop Rings, J. Algebra 183 (1996), 637–648.
A.A. Bovdi, Z.S. Marciniak, S.K. Sehgal, Torsion Units in Infinite Group Rings, J. Number Theory 47 (1994), 284–299.
O. Chein and E.G. Goodaire, Loops whose Loop Rings are Alternative, Comm, in Algebra, 14 (1986), 293–310.
O. Chein and E.G. Goodaire, Loops whose Loop Rings in characteristic 2 are Alternative, Comm. in Algebra, 18(3) (1990), 659–688.
E.G. Goodaire, E. Jespers and C. Polcino Milies, “Alternative Loop Rings”, North Holland Math. Series 184, Elsevier, Amsterdam, (1996).
E.G. Goodaire and M. M. Parmenter, Units in Alternative Loop Rings, Israel J. of Math. 53 (1986), 209–216.
E.G. Goodaire and C. Polcino Milies, Isomorphism of Integral Loop Rings, Rend. Circ. Mat. Palermo XXXVII (1988), 126–135.
E.G. Goodaire and C. Polcino Milies, Torsion Units in Alternative Loops, Proc. Amer. Math. Soc. 107 (1989) 7–15.
E.G. Goodaire and C. Polcino Milies, The Torsion Product Property in Alternative Algebras, RT-MAT 95-15.
E.G. Goodaire and C. Polcino Milies, Finite Conjugacy in Alternative Loop Algebras, Comm. Algebra 24 (3), (1996), 881–889.
E.G. Goodaire and C. Polcino Milies, Ring Alternative Loops and their Loop Rings, Resenhas IME-USP 2 (1996), No. 1, 47–82.
E.G. Goodaire and C. Polcino Milies, On the Loop of Units of Alternative Loop Rings, Nova J. Alg. Geom. Game Theory, to appear.
E.G. Goodaire and C. Polcino Milies, Central Idempotents in Alternative Loop Algebras, preprint.
S.O. Juriaans, Trace Properties of Torsion Units in Group Rings II, preprint.
G. Leal and C. Polcino Milies, Isomorphic Group (and Loop) Algebras, J. Algebra 155 (1), (1993), 195–210.
S.K. Sehgal, “Units of Integral Group Rings”, Longman’s, Essex, 1993.
S.K. Sehgal, “Topics in Group Rings”, Marcel Decker Inc. New York and Basel, 1978.
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by CNPq (Proc. 300411/94)
Partially supported by Fapesp (Proc. 95/2844-1)
Rights and permissions
About this article
Cite this article
de Barros, L.G.X., Juriaans, S.O. Units in Alternative Integral Loop Rings. Results. Math. 31, 266–281 (1997). https://doi.org/10.1007/BF03322164
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03322164