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Finite Generation of Units in Alternative Loop Rings

✍ Scribed by Edgar G. Goodaire; Guilherme Leal; César Polcino Milies

Publisher
Springer
Year
2006
Tongue
English
Weight
129 KB
Volume
120
Category
Article
ISSN
0025-2611

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📜 SIMILAR VOLUMES

Alternative Loop Rings with Solvable Uni
Alternative Loop Rings with Solvable Unit Loops
✍ Edgar G Goodaire; César Polcino Milies 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 129 KB

Let L be an RA loop, that is, a loop whose loop ring in any characteristic is an alternative, but not associative, ring. We find necessary and sufficient conditions Ž . for the Moufang unit loop of RL to be solvable when R is the ring of rational integers or an arbitrary field.

Units in Integral Loop Rings
Units in Integral Loop Rings
✍ Luiz G.X. de Barros; Stanley O. Juriaans 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 161 KB

Higman has proved a classical result giving necessary and sufficient conditions for the units of an integral group ring to be trivial. In this paper we extend this result to loop rings of some diassociative loops.