scholarly journals REMARKS ON EISENSTEIN

2013 ◽  
Vol 94 (2) ◽  
pp. 158-180 ◽  
Author(s):  
YURI BILU ◽  
ALEXANDER BORICHEV
Keyword(s):  
Power Series ◽  
Number Field ◽  
Laurent Series ◽  
Quantitative Version ◽  
Algebraic Power Series

AbstractWe obtain a fully explicit quantitative version of the Eisenstein theorem on algebraic power series which is more suitable for certain applications than the existing version due to Dwork, Robba, Schmidt and van der Poorten. We also treat ramified series and Laurent series, and we demonstrate some applications; for instance, we estimate the discriminant of the number field generated by the coefficients.

A Gap Theorem for Differentially Algebraic Power Series

Number Theory ◽  
1991 ◽  
pp. 211-214
Author(s):  
Leonard Lipshitz ◽  
Lee A. Rubel
Keyword(s):  
Power Series ◽  
Gap Theorem ◽  
Algebraic Power Series

Some remarks on formal power series and formal Laurent series

2017 ◽  
Vol 67 (3) ◽  
Author(s):  
Dariusz Bugajewski ◽  
Xiao-Xiong Gan
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Laurent Series ◽  
Formal Laurent Series ◽  
Formal Power

AbstractIn this article we consider the topology on the set of formal Laurent series induced by the ultrametric defined via the order. In particular, we establish that the product of formal Laurent series, considered in [GAN, X. X.—BUGAJEWSKI, D.:

scholarly journals Goldie twisted partial skew power series rings

2019 ◽  
Vol 18 (08) ◽  
pp. 1950151 ◽  
Author(s):  
Wagner Cortes ◽  
Simone Ruiz
Keyword(s):  
Power Series ◽  
Laurent Series ◽  
Prime Radical ◽  
Prime Ideals ◽  
Partial Action ◽  
Unital Ring ◽  
Power Series Rings

In this paper, we work with a unital twisted partial action of [Formula: see text] on a unital ring [Formula: see text]. We introduce the twisted partial skew power series rings and twisted partial skew Laurent series rings. We study primality, semi-primality and the prime ideals in these rings. We describe the prime radical in twisted partial skew Laurent series rings. We investigate the Goldie property in twisted partial skew power series rings and twisted partial skew Laurent series rings. Moreover, we describe conditions for the semiprimality in twisted partial skew power series rings.

Sign in / Sign up

Export Citation Format

Share Document