This book contains the definitions of several ring constructions used in various applications.
The concept of a groupoid-graded ring includes many of these constructions as special …

GROUP ALGEBRAS WHOSE UNITS SATISFY A GROUP IDENTITY 1. Introduction The unit
group U = U(FG) is said to satisfy a group identity Page 1 PROCEEDINGS OF THE AMERICAN …

Publisher Summary This chapter discusses the theory of group rings, given by Sir William
Rowan Hamilton. It is the first formal theory of complex numbers, defining them as ordered …

Let A be an algebraic algebra over an infinite field K and let U (A) be its group of units. We
prove a stronger version of Hartley's conjecture for A, namely, if a Laurent polynomial …

Abstract Marciniak and Sehgal (Marciniak, Z., Sehgal, SK (1997). Constructing free
subgroups of integral group rings units. Proc. Amer. Math. Soc. 125 (4): 1005–1009) …

Groups generated by a Bass cyclic unit and a bicyclic unit in the units of Z[G] Page 1 J. Group
Theory 7 (2004), 421–430 Journal of Group Theory ( de Gruyter 2004 Groups generated by a …

Let FG be the group ring of a group G over a field F of characteristic p≥ 0. Let* be the
natural involution, γ=∑ γ (g) g→ γ*=∑ γ (g) g-1. Let us denote by (KG)+= γ∈ FG: γ*= γ and …

Let R be an associative algebra and U (R) its group of units. It is in general a difficult
problem to relate the structure of U (R) to that of R; for instance, can one understand the …

1 Introduction Page 1 Resenhas IME-USP 1996, Vol. 2, No. 3, 275 - 282. Units of Group Rings
and Their Group Identities 1 Antonio Giambruno Abstract: This paper surveys recent results …

CROUP AL, C, EE. H. AS VV HOS E UNITS Page 1 PROCEEDINCE OF THE AMERICAN
MATHEMATICAL, SOCIETY Volurne 125, Nurnber 3, March 1997, Pages 629–634 S 0002-9939 …