Skew fields with involution having only one unitary element

1979 ◽  
Vol 2 (1-2) ◽  
pp. 119-123
Author(s):  
P. M. Cohn
Keyword(s):  
Unitary Element ◽  
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.

scholarly journals A note on liftings of hermitian elements and unitaries

1980 ◽  
Vol 21 (1) ◽  
pp. 183-185
Author(s):  
C. K. Fong
Keyword(s):  
Banach Algebra ◽  
Present Note ◽  
Partial Answer ◽  
General Question ◽  
Quotient Mapping ◽  
Unitary Element ◽  
Finite Dimensional ◽  
Complex Banach Algebra ◽  
Special Cases

Let A be a complex Banach algebra with unit 1 satisfying ∥1∥ = 1. An element u in A is said to be unitary if it is invertible and ∥u∥ = ∥u−1∥ = 1. An element h in A is said to be hermitian if ∥exp(ith)∥ = 1 for all real t; that is, exp(ith) is unitary for all real t. Suppose that J is a closed two-sided ideal and π: A → A/J is the quotient mapping. It is easy to see that if x in A is hermitian (resp. unitary), then so is π(x) in A/J. We consider the following general question which is the converse of the above statement: given a hermitian (resp. unitary) element y in A/J, can we find a hermitian (resp. unitary) element x in A such that π(x)=y? (The author has learned that this question, in a more restrictive form, was raised by F. F. Bonsall and that some special cases were investigated; see [1], [2].) In the present note, we give a partial answer to this question under the assumption that A is finite dimensional.

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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