<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Let <italic>S</italic> be a domain and <italic>R</italic> = <italic>S</italic>[<italic>t</italic>; <italic>σ, δ</italic>] a skew polynomial ring, where <italic>σ</italic> is an injective endomorphism of <italic>S</italic> and <italic>δ</italic> a left <italic>σ</italic> -derivation. We give criteria for skew polynomials <italic>f</italic> ∈ <italic>R</italic> of degree less or equal to four to be irreducible. We apply them to low degree polynomials in quantized Weyl algebras and the quantum planes. We also consider <italic>f</italic>(<italic>t</italic>) = <italic>t<sup>m</sup></italic> − <italic>a</italic> ∈ <italic>R</italic>.</p>
</abstract>

Let S be a domain and R = S[t; σ, δ] a skew polynomial ring, where σ is an injective endomorphism of S and δ a left σ -derivation. We give criteria for skew polynomials f ∈ R of degree less or equal to four to be irreducible. We apply them to low degree polynomials in quantized Weyl algebras and the quantum planes. We also consider f(t) = tm − a ∈ R.

Irreducible skew polynomials over domains

University of Nottingham, University Park

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Irreducible skew polynomials over domains"}

Let S be a domain and R = S[t; σ, δ] a skew polynomial ring, where σ is an injective endomorphism of S and δ a left σ -derivation. We give criteria for skew...

Irreducible skew polynomials over domains

Published Online: Nov 23, 2021

Page range: 75 - 89

Received: Apr 22, 2021

Accepted: Apr 30, 2021

DOI: https://doi.org/10.2478/auom-2021-0035

Keywords
Skew polynomials, irreducible polynomials

© 2021 C. Brown et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Irreducible skew polynomials over domains

Published Online: Nov 23, 2021

Page range: 75 - 89

Received: Apr 22, 2021

Accepted: Apr 30, 2021

DOI: https://doi.org/10.2478/auom-2021-0035

KeywordsSkew polynomials, irreducible polynomials

© 2021 C. Brown et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Skew polynomials, irreducible polynomials