Local polynomial functions on factor rings of the integers
نویسندگان
چکیده
منابع مشابه
Polynomial Functions over Rings of Residue Classes of Integers
In this thesis we discuss how to find equivalent representations of polynomial functions over the ring of integers modulo a power of a prime. Specifically, we look for lower degree representations and representations with fewer variables for which important applications in electrical and computer engineering exist. We present several algorithms for finding these compact formulations. INDEX WORD...
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Every function on a nite residue class ring D=I of a Dedekind domain D is induced by an integer-valued polynomial on D that preserves congruences mod I if and only if I is a power of a prime ideal. If R is a nite commutative local ring with maximal ideal P of nilpotency N satisfying for all a; b 2 R, if ab 2 Pn then a 2 P k , b 2 P j with k + j min(n;N), we determine the number of functions (as...
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An algorithm is presented to compute the minimal associated primes of an ideal in a polynomial ring over the integers. It differs from the known algorithms insofar as it avoids having to compute Gröbner bases over the integers until the very end, thereby eliminating one of the bottlenecks of those algorithms. © 2011 Elsevier Ltd. All rights reserved.
متن کاملIdeal Membership in Polynomial Rings over the Integers
We will reproduce a proof, using Hermann’s classical method, in Section 3 below. Note that the computable character of this bound reduces the question of whether f0 ∈ (f1, . . . , fn) for given fj ∈ F [X ] to solving an (enormous) system of linear equations over F . Hence, in this way one obtains a (naive) algorithm for solving the ideal membership problem for F [X ] (provided F is given in som...
متن کاملساختار کلاسهایی از حلقه های z- موضعی و c- موضعی the structure of some classes of z-local and c-local rings
فرض کنیمr یک حلقه تعویض پذیر ویکدار موضعی باشدو(j(r رایکال جیکوبسن r و(z(r مجموعه مقسوم علیه های صفر حلقه r باشد.گوییم r یک حلقه z- موضعی است هرگاه j(r)^2=. .همچنین برای یک حلقه تعویض پذیر r فرض کنیم c یک عنصر ناصفر از (z( r باشد با این خاصیت که cz( r)=0 گوییم حلقه موضعی r یک حلقه c - موضعی است هرگاه و{0 و z(r)^2={cو z(r)^3=0, نیز xz( r)=0 نتیجه دهد که x عضو {c,0 } است. در این پایان نامه ساخ...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1979
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700012155