Projective generation of ideals in polynomial extensions

2020 ◽  
Vol 12 (3) ◽  
pp. 333-352
Author(s):  
Manoj K. Keshari ◽  
Md. Ali Zinna
Keyword(s):  
Polynomial Extensions

scholarly journals The radiation instability in modified gravity

2021 ◽  
Vol 36 (08n09) ◽  
pp. 2150060
Author(s):  
Spiros Cotsakis ◽  
Dimitrios Trachilis
Keyword(s):  
General Relativity ◽  
General Solution ◽  
Modified Gravity ◽  
Evolution Equations ◽  
Formal Series ◽  
Series Expansions ◽  
General Polynomial ◽  
Theories Of Gravity ◽  
Polynomial Extensions

We study the problem of the instability of inhomogeneous radiation universes in quadratic Lagrangian theories of gravity written as a system of evolution equations with constraints. We construct formal series expansions and show that the resulting solutions have a smaller number of arbitrary functions than that required in a general solution. These results continue to hold for more general polynomial extensions of general relativity.

scholarly journals Skew Polynomial Extensions over Zip Rings

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Wagner Cortes
Keyword(s):  
Polynomial Extension ◽  
Armendariz Rings ◽  
Skew Polynomial ◽  
The Relationship ◽  
Polynomial Extensions

In this article, we study the relationship between left (right) zip property of and skew polynomial extension over , using the skew versions of Armendariz rings.

π-Rickart rings

2020 ◽  
pp. 2150137
Author(s):  
Gary F. Birkenmeier ◽  
Yeliz Kara ◽  
Adnan Tercan
Keyword(s):  
Matrix Rings ◽  
Full Matrix ◽  
Provided Examples ◽  
Polynomial Extensions

In this paper, we introduce and investigate three new versions of the Rickart condition for rings. These conditions, as well as, three new corresponding regularities are defined using projection invariance. We show how these conditions relate to each other as well as their connections to the well-known Baer, Rickart, quasi-Baer, p.q.-Baer, regular, and biregular conditions. Applications to polynomial extensions and to triangular and full matrix rings are provided. Examples illustrate and delimit results.

INVARIANTS OF DEFECTLESS IRREDUCIBLE POLYNOMIALS

2010 ◽  
Vol 09 (04) ◽  
pp. 603-631 ◽  
Author(s):  
RON BROWN ◽  
JONATHAN L. MERZEL
Keyword(s):  
Irreducible Polynomial ◽  
Newton Polygon ◽  
Extension Field ◽  
Irreducible Polynomials ◽  
Technical Result ◽  
Valued Field ◽  
Minimal Pairs ◽  
Simple Characterization ◽  
Polynomial Extensions

Defectless irreducible polynomials over a Henselian valued field (F, v) have been studied by means of strict systems of polynomial extensions and complete (also called "saturated") distinguished chains. Strong connections are developed here between these two approaches and applications made to both. In the tame case in which a root α of an irreducible polynomial f generates a tamely ramified extension of (F, v), simple formulas are given for the Krasner constant, the Brink separant and the diameter of f. In this case a (best possible) result is given showing that a sufficiently good approximation in an extension field K of F to a root of a defectless polynomial f over F guarantees the existence of an exact root of f in K. Also in the tame case a (best possible) result is given describing when a polynomial is sufficiently close to a defectless polynomial so as to guarantee that the roots of the two polynomials generate the same extension fields. Another application in the tame case gives a simple characterization of the minimal pairs (in the sense of N. Popescu et al.). A key technical result is a computation in the tame case of the Newton polygon of f(x+α). Invariants of defectless polynomials are discussed and the existence of defectless polynomials with given invariants is proven. Khanduja's characterization of the tame polynomials whose Krasner constants equal their diameters is generalized to arbitrary defectless polynomials. Much of the work described here will be seen not to require the hypothesis that (F, v) is Henselian.

scholarly journals Polynomial extensions of semistar operations

2013 ◽  
Vol 390 ◽  
pp. 250-263
Author(s):  
Gyu Whan Chang ◽  
Marco Fontana ◽  
Mi Hee Park
Keyword(s):  
Polynomial Extensions
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