Puiseux Expansions in Nonzero Characteristic

2004 ◽  
pp. 767-774
Author(s):  
Sanju Vaidya
Keyword(s):  
Nonzero Characteristic ◽  
Puiseux Expansions

scholarly journals CHARACTER CLUSTERS FOR LIE ALGEBRA MODULES OVER A FIELD OF NONZERO CHARACTERISTIC

2013 ◽  
Vol 89 (2) ◽  
pp. 234-242 ◽  
Author(s):  
DONALD W. BARNES
Keyword(s):  
Lie Algebra ◽  
Saturated Formation ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Direct Sum ◽  
Finite Dimensional ◽  
Nonzero Characteristic ◽  
Composition Factors

AbstractFor a Lie algebra $L$ over an algebraically closed field $F$ of nonzero characteristic, every finite dimensional $L$-module can be decomposed into a direct sum of submodules such that all composition factors of a summand have the same character. Using the concept of a character cluster, this result is generalised to fields which are not algebraically closed. Also, it is shown that if the soluble Lie algebra $L$ is in the saturated formation $\mathfrak{F}$ and if $V, W$ are irreducible $L$-modules with the same cluster and the $p$-operation vanishes on the centre of the $p$-envelope used, then $V, W$ are either both $\mathfrak{F}$-central or both $\mathfrak{F}$-eccentric. Clusters are used to generalise the construction of induced modules.

scholarly journals An algebraically closed field

1968 ◽  
Vol 9 (2) ◽  
pp. 146-151 ◽  
Author(s):  
F. J. Rayner
Keyword(s):  
Positive Integer ◽  
Power Series ◽  
Formal Power Series ◽  
Characteristic Zero ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Zero Characteristic ◽  
Image Position ◽  
Formal Power ◽  
Puiseux Expansions

Letkbe any algebraically closed field, and denote byk((t)) the field of formal power series in one indeterminatetoverk. Letso thatKis the field of Puiseux expansions with coefficients ink(each element ofKis a formal power series intl/rfor some positive integerr). It is well-known thatKis algebraically closed if and only ifkis of characteristic zero [1, p. 61]. For examples relating to ramified extensions of fields with valuation [9, §6] it is useful to have a field analogous toKwhich is algebraically closed whenkhas non-zero characteristicp. In this paper, I prove that the setLof all formal power series of the form Σaitei(where (ei) is well-ordered,ei=mi|nprt,n∈ Ζ,mi∈ Ζ,ai∈k,ri∈ Ν) forms an algebraically closed field.

Tits' work on unipotent groups in nonzero characteristic

2015 ◽  
pp. 561-580
Author(s):  
Brian Conrad ◽  
Ofer Gabber ◽  
Gopal Prasad
Keyword(s):  
Unipotent Groups ◽  
Nonzero Characteristic

Tits' work on unipotent groups in nonzero characteristic

2011 ◽  
pp. 473-493
Author(s):  
Brian Conrad ◽  
Ofer Gabber ◽  
Gopal Prasad
Keyword(s):  
Unipotent Groups ◽  
Nonzero Characteristic

scholarly journals On the estimation of coefficients of irreducible factors of polynomials over a field of formal power series in nonzero characteristic

2019 ◽  
Vol 489 (3) ◽  
pp. 232-234
Author(s):  
A. L. Chistov
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
New Method ◽  
Arbitrary Characteristic ◽  
Nonzero Characteristic ◽  
Formal Power ◽  
Roots Of A Polynomial

We discuss some problems and results related to the Newton-Puiseux algorithm and its generalization for nonzero characteristic obtained by the author earlier. A new method is suggested for obtaining effective estimations of the roots of a polynomial in the field of fraction-power series in arbitrary characteristic.

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