منابع مشابه
The Units of Group-rings
when addition and multiplication are defined in the obvious way, form a ring, the group-ring of G over K, which will be denoted by R (G, K). Henceforward, we suppose that K has the modulus 1, and we denote the identity in G by e0. Then R(G,K) has the modulus l.e0. Since no confusion can arise thereby, the element 1. e in R(G, K) will be written as e, and whenever it is convenient, the elements ...
متن کاملInvolutions and Free Pairs of Bass Cyclic Units in Integral Group Rings
Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let ∗ be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (uk,m(x), uk,m(x ∗)), or (uk,m(x), uk,m(y)), formed respectively by Bass cyclic and ∗-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG. 1....
متن کاملArithmetic Rigidity and Units in Group Rings
For any finite group G the group U(Z[G]) of units in the integral group ring Z[G] is an arithmetic group in a reductive algebraic group, namely the Zariski closure of SL1(Q[G]). In particular, the isomorphism type of the Q-algebra Q[G] determines the commensurability class of U(Z[G]); we show that, to a large extent, the converse is true. In fact, subject to a certain restriction on the Q-repre...
متن کاملLinearly Compact Rings Having a Simple Group of Units
Those linearly compact rings with identity having a simple group of units and a transsnitely nilpotent Jacobson radical are identiied. A consequence of this characterization is Cohen and Koh's classiication theorem for compact rings with identity having a simple group of units.
متن کاملCyclic Group Actions on Polynomial Rings
We consider a cyclic group of order p acting on a module incharacteristic p and show how to reduce the calculation of the symmetric algebra to that of the exterior algebra. Consider a cyclic group of order p acting on a polynomial ring S = k[x1, . . . , xr], where k is a field of characteristic p; this is equivalent to the symmetric algebra S∗(V ) on the module V generated by x1, . . . , xr. We...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1970
ISSN: 0021-8693
DOI: 10.1016/0021-8693(70)90030-x