Constructible units in abelian p-group rings
نویسندگان
چکیده
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 ...
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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...
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Let R be a noetherian ring, and G(R) the Grothendieck group of finitely generated modules over R. For a finite abelian group n, we describe G(Rn) as the direct sum of groups G(R’). Each R’ is the form RI<,,, I/n], where n is a positive integer and Cn a primitive nth root of unity. As an application, we describe the structure of the Grothendieck group of pairs (H. u), where His an abelian group ...
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Let R be the valuation ring ofK, a finite extension of Qp containing a primitive pth root of unity, and let G be an elementary abelian p-group of order p, with dual group Ĝ. We construct a new family of triangular Hopf orders over R in KG, a proper subfamily whose duals are also triangular, and a proper subfamily of that family whose construction extends the truncated exponential construction o...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1990
ISSN: 0022-4049
DOI: 10.1016/0022-4049(90)90088-y