Extensions of valuations on skew fields

1980 ◽  
pp. 28-41 ◽  
Author(s):  
P. M. Cohn ◽  
M. Mahdavi-Hezavehi
Keyword(s):  
Skew Fields

Skew Fields

1983 ◽  
Author(s):  
P. K. Draxl
Keyword(s):  
Skew Fields

On embedding some G-filtered rings into skew fields

2014 ◽  
Vol 55 (6) ◽  
pp. 1017-1041
Author(s):  
A. I. Valitskas
Keyword(s):  
Skew Fields

scholarly journals HIGHER PRODUCT PYTHAGORAS NUMBERS OF SKEW FIELDS

2010 ◽  
Vol 03 (01) ◽  
pp. 193-207
Author(s):  
Dejan Velušček
Keyword(s):  
Laurent Series ◽  
Skew Field ◽  
Skew Fields ◽  
Pythagoras Number

We introduce the n–th product Pythagoras number p n(D), the skew field analogue of the n–th Pythagoras number of a field. For a valued skew field (D, v) where v has the property of preserving sums of permuted products of n–th powers when passing to the residue skew field k v and where Newton's lemma holds for polynomials of the form Xn - a, a ∈ 1 + I v , p n(D) is bounded above by either p n( k v ) or p n( k v ) + 1. Spherical completeness of a valued skew field (D, v) implies that the Newton's lemma holds for Xn - a, a ∈ 1 + I v but the lemma does not hold for arbitrary polynomials. Using the above results we deduce that p n (D((G))) = p n(D) for skew fields of generalized Laurent series.

Linear operators preserving idempotence on matrices spaces over skew-fields

1997 ◽  
Vol 42 (15) ◽  
pp. 1244-1247
Author(s):  
Shaowu Liu ◽  
Guifang Yuan
Keyword(s):  
Linear Operators ◽  
Skew Fields

On Free Subobjects of Skew Fields

1984 ◽  
pp. 281-285 ◽  
Author(s):  
Leonid Makar-Limanov
Keyword(s):  
Skew Fields
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