scholarly journals The Whitehead group of a polynomial extension

1964 ◽  
Vol 22 (1) ◽  
pp. 61-79 ◽  
Author(s):  
H. Bass ◽  
A. Heller ◽  
R. G. Swan
Keyword(s):  
Whitehead Group ◽  
Polynomial Extension

scholarly journals Polynomial Extension Operators. Part I

2008 ◽  
Vol 46 (6) ◽  
pp. 3006-3031 ◽  
Author(s):  
Leszek Demkowicz ◽  
Jayadeep Gopalakrishnan ◽  
Joachim Schöberl
Keyword(s):  
Polynomial Extension

A Geometric Construction of the Boundedly Controlled Whitehead Group

2020 ◽  
pp. 13-26
Author(s):  
Douglas R. Anderson ◽  
Hans Jørgen Munkholm
Keyword(s):  
Geometric Construction ◽  
Whitehead Group

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.

scholarly journals Unique factorisation rings

1992 ◽  
Vol 35 (2) ◽  
pp. 255-269 ◽  
Author(s):  
A. W. Chatters ◽  
M. P. Gilchrist ◽  
D. Wilson
Keyword(s):  
Prime Ideal ◽  
Prime Ring ◽  
Polynomial Identity ◽  
Noetherian Ring ◽  
Basic Theory ◽  
Maximal Order ◽  
Prime Element ◽  
Polynomial Extension ◽  
Simple Ring ◽  
Left And Right

Let R be a ring. An element p of R is a prime element if pR = Rp is a prime ideal of R. A prime ring R is said to be a Unique Factorisation Ring if every non-zero prime ideal contains a prime element. This paper develops the basic theory of U.F.R.s. We show that every polynomial extension in central indeterminates of a U.F.R. is a U.F.R. We consider in more detail the case when a U.F.R. is either Noetherian or satisfies a polynomial identity. In particular we show that such a ring R is a maximal order, that every height-1 prime ideal of R has a classical localisation in which every two-sided ideal is principal, and that R is the intersection of a left and right Noetherian ring and a simple ring.

Triviality of the reduced Whitehead group over certain fields

1978 ◽  
Vol 24 (5) ◽  
pp. 836-841
Author(s):  
V. A. Lipnitskii
Keyword(s):  
Whitehead Group

scholarly journals Polynomial extension property in the classical Cartan domain $${\mathcal {R}_{II}}$$

2020 ◽  
Vol 115 (6) ◽  
pp. 657-666
Author(s):  
Krzysztof Maciaszek
Keyword(s):  
Extension Property ◽  
Algebraic Subset ◽  
Polynomial Extension ◽  
Cartan Domain ◽  
Holomorphic Retract

AbstractIn this work, it is shown that for the classical Cartan domain $$\mathcal {R}_{II}$$ R II consisting of symmetric $$2\times 2$$ 2 × 2 matrices, every algebraic subset of $$\mathcal {R}_{II}$$ R II , which admits the polynomial extension property, is a holomorphic retract.

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