Combining Euclidean and adequate 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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All rings R considered are commutative and have an identity element. Contessa called R a VNL-ring if a or 1 a has a Von Neumann inverse whenever a 2 R. Sample results: Every prime ideal of a VNL-ring is contained in a unique maximal ideal. Local and Von Neumann regular rings are VNL and if the product of two rings is VNL, then both are Von Neumann regular, or one is Von Neumann regular and the ...
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The binary operation multint on Z is defined as follows: (Def. 1) For all elements a, b of Z holds (multint)(a, b) = ·R(a, b). The unary operation compint on Z is defined as follows: (Def. 2) For every element a of Z holds (compint)(a) = −R(a). The double loop structure INT.Ring is defined by: (Def. 3) INT.Ring = 〈Z, +Z,multint, 1(∈ Z), 0(∈ Z)〉. Let us mention that INT.Ring is strict and non em...
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The search for an adequate dose involves some of the most complex series of decisions to be made in developing a clinically viable product. Typically decisions based on such dose-finding studies reside in two domains: the first being one of “proof” that the treatment provides evidence of effectiveness. The second concerns the need to choose dose(s) for further development. The analysis of dose ...
متن کاملOn Signature-Based Gröbner Bases Over Euclidean Rings
In this paper we present first steps in using signature-based Gröbner basis algorithms like Faugère’s F5 or GVW for computation over Euclidean rings. We present problems appearing when having to deal with coefficients and zero divisors and give practical solution techniques. A hybrid algorithm is presented trying to combine the advantages of signature-based and non-signature-based Gröbner basis...
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ژورنال
عنوان ژورنال: TURKISH JOURNAL OF MATHEMATICS
سال: 2016
ISSN: 1300-0098,1303-6149
DOI: 10.3906/mat-1502-58