A NOTE ON GIRSTMAIR’S IRREDUCIBILITY CRITERION

2021 ◽  
pp. 1-5
Author(s):  
JITENDER SINGH ◽  
SANJEEV KUMAR
Keyword(s):  
Irreducibility Criterion

Abstract Girstmair [‘On an irreducibility criterion of M. Ram Murty’, Amer. Math. Monthly112(3) (2005), 269–270] gave a generalisation of Ram Murty’s irreducibility criterion. We further generalise these criteria.

scholarly journals ON IRREDUCIBLE FACTORS OF POLYNOMIALS OVER COMPLETE FIELDS

2012 ◽  
Vol 12 (01) ◽  
pp. 1250125 ◽  
Author(s):  
SUDESH K. KHANDUJA ◽  
SANJEEV KUMAR
Keyword(s):  
Algebraic Number ◽  
Number Fields ◽  
Manuscripta Math ◽  
Algebraic Number Fields ◽  
Valued Fields ◽  
Valued Field ◽  
Transcendental Extension ◽  
Simple Transcendental Extension ◽  
Irreducibility Criterion ◽  
Hensel’S Lemma

Let (K, v) be a complete rank-1 valued field. In this paper, we extend classical Hensel's Lemma to residually transcendental prolongations of v to a simple transcendental extension K(x) and apply it to prove a generalization of Dedekind's theorem regarding splitting of primes in algebraic number fields. We also deduce an irreducibility criterion for polynomials over rank-1 valued fields which extends already known generalizations of Schönemann Irreducibility Criterion for such fields. A refinement of Generalized Akira criterion proved in Khanduja and Khassa [Manuscripta Math.134(1–2) (2010) 215–224] is also obtained as a corollary of the main result.

On a generalization of Eisenstein's irreducibility criterion

Mathematika ◽  
1997 ◽  
Vol 44 (1) ◽  
pp. 37-41 ◽  
Author(s):  
Sudesh K. Khanduja ◽  
Jayanti Saha
Keyword(s):  
Irreducibility Criterion

scholarly journals Constructing irreducible polynomials with prescribed level curves over finite fields

2001 ◽  
Vol 27 (4) ◽  
pp. 197-200
Author(s):  
Mihai Caragiu
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Irreducible Polynomial ◽  
Irreducible Polynomials ◽  
Level Curves ◽  
Curves Over Finite Fields ◽  
Irreducibility Criterion ◽  
Absolutely Irreducible Polynomial

We use Eisenstein's irreducibility criterion to prove that there exists an absolutely irreducible polynomialP(X,Y)∈GF(q)[X,Y]with coefficients in the finite fieldGF(q)withqelements, with prescribed level curvesXc:={(x,y)∈GF(q)2|P(x,y)=c}.

scholarly journals An irreducibility criterion for power series

2017 ◽  
Vol 145 (11) ◽  
pp. 4731-4739 ◽  
Author(s):  
Guillaume Rond ◽  
Bernd Schober
Keyword(s):  
Power Series ◽  
Irreducibility Criterion

scholarly journals Irreducibility criterion for certain trinomials

2019 ◽  
Vol S (1) ◽  
pp. 116-119
Author(s):  
Biswajit Koley ◽  
A. Satyanarayana Reddy
Keyword(s):  
Irreducibility Criterion

An Irreducibility Criterion for Polynomials Over the Integers

1969 ◽  
Vol 76 (7) ◽  
pp. 795-797 ◽  
Author(s):  
W. S. Brown ◽  
R. L. Graham
Keyword(s):  
Irreducibility Criterion

On the Abhyankar–Moh irreducibility criterion for quasi-ordinary polynomials

2021 ◽  
Vol 164 (1) ◽  
pp. 149-160
Author(s):  
Beata Gryszka ◽  
Janusz Gwoździewicz
Keyword(s):  
Irreducibility Criterion
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