Some Algebraic Properties of Polynomial Rings

被引：3

作者：

Schwarzweller, Christoph ^{[1
]}

Kornilowicz, Artur ^{[2
]}

Rowinska-Schwarzweller, Agnieszka

机构：

[1] Univ Gdansk, Inst Comp Sci, Gdansk, Poland

[2] Univ Bialystok, Inst Informat, Bialystok, Poland

来源：

FORMALIZED MATHEMATICS | 2016年 / 24卷 / 03期

关键词：

polynomial; polynomial ring; polynomial GCD;

D O I：

10.1515/forma-2016-0019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/< p > is isomorphic to the field of polynomials with degree smaller than the one of p.

引用

页码：227 / 237

页数：11

共 50 条

[11] ALGEBRAIC CONJUGACY CLASSES AND SKEW POLYNOMIAL-RINGS
LAM, TY
LEROY, A
PERSPECTIVES IN RING THEORY, 1988, 233 : 153 - 203
[12] COHERENCE OF POLYNOMIAL RINGS OVER SEMISIMPLE ALGEBRAIC ALGEBRAS
CARSON, AB
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 34 (01) : 20 - &
[13] The Transfer of Some Algebraic Properties on Skew Generalized Power Series Rings
Fahmy, M. H.
Salem, R. M.
Shehata, Shaimaa Sh
SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2021, 45 (01) : 43 - 54
[14] Algebraic properties of necklace rings
Parmenter, MM
Spiegel, E
COMMUNICATIONS IN ALGEBRA, 1998, 26 (05) : 1625 - 1632
[15] RADICAL PROPERTIES OF POLYNOMIAL RINGS
KREMPA, J
BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES MATHEMATIQUES ASTRONOMIQUES ET PHYSIQUES, 1972, 20 (07): : 545 - &
[16] Algorithmic properties of polynomial rings
Kalkbrener, M
JOURNAL OF SYMBOLIC COMPUTATION, 1998, 26 (05) : 525 - 581
[17] ON COMMUTATIVITY OF RINGS WITH SOME POLYNOMIAL CONSTRAINTS
ASHRAF, M
QUADRI, MA
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1990, 41 (02) : 201 - 206
[18] Some simple derivations of polynomial rings
Kesarwany, Ashish Kumar
Wagh, Vinay
JOURNAL OF THE RAMANUJAN MATHEMATICAL SOCIETY, 2024, 39 (01)
[19] Some results on retracts of polynomial rings
Chakraborty, Sagnik
Dasgupta, Nikhilesh
Dutta, Amartya Kumar
Gupta, Neena
JOURNAL OF ALGEBRA, 2021, 567 : 243 - 268
[20] SOME RESULTS ON QUATERNION POLYNOMIAL RINGS
MORTON, M
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (05): : A504 - A505

← 1 2 3 4 5 →