Arithmetic euclidean rings
نویسندگان
چکیده
منابع مشابه
About Euclidean Rings
In this article all rings are commutative with unit, all modules are unitary. Given a ring A, its multiplicative group of units (i.e. invertible elements) is denoted by A*. The customary definition of a Euclidean ring is that it is a domain A together with a map F : A + N (the nonnegative integers) such that (1) I : p(a) for a, b E r3 (0); (2) given a, b E -‘-I, b m;’ 0, there exist q and Y in ...
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Circular arithmetic, introduced by I. Gargantini and P. Henrici [2J as an extension of the complex arithmetic, provided the formulati on of methods for solving some problems of computational complex anal ysis (e. g. tl:e inclusion of the polynomial complex zeros [2J, [3J, cir cular approximation of the closed regions in the complex plane [IJ, [4J , ~J, [8J, the evaluations of complex functio...
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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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It is shown that every commutative arithmetic ring R has λ-dimension ≤ 3. An example of a commutative Kaplansky ring with λ-dimension 3 is given. Moreover, if R satisfies one of the following conditions, semi-local, semi-prime, self f p-injective, zero-Krull dimensional, CF or FSI then λ-dim(R) ≤ 2. It is also shown that every zero-Krull dimensional commu-tative arithmetic ring is a Kaplansky r...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1974
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-26-1-105-113