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

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 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.

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.

scholarly journals Polynomial extension of Fleck's congruence

2006 ◽  
Vol 122 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Zhi-Wei Sun
Keyword(s):  
Polynomial Extension

scholarly journals Automorphisms for Some Symmetric Multiparameter Quantized Weyl Algebras and Their Localizations

2017 ◽  
Vol 24 (03) ◽  
pp. 419-438 ◽  
Author(s):  
Xin Tang
Keyword(s):  
Automorphism Group ◽  
Weyl Algebra ◽  
Isomorphism Problem ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Polynomial Extension ◽  
Localization Formula ◽  
Weyl Algebras ◽  
Necessary And Sufficient ◽  
Quantized Weyl Algebra

We study a family of “symmetric” multiparameter quantized Weyl algebras [Formula: see text] and some related algebras. We compute the Nakayama automorphism of [Formula: see text], give a necessary and sufficient condition for [Formula: see text] to be Calabi-Yau, and prove that [Formula: see text] is cancellative. We study the automorphisms and isomorphism problem for [Formula: see text] and [Formula: see text]. Similar results are established for the Maltsiniotis multiparameter quantized Weyl algebra [Formula: see text] and its polynomial extension. We prove a quantum analogue of the Dixmier conjecture for a simple localization [Formula: see text] and determine its automorphism group.

scholarly journals A New Method of the Logical Functions Minimization in the Polynomial Set-Theoretical Format. «Handshaking» Procedure

2021 ◽  
pp. 03-14
Author(s):  
Bohdan Ye. Rytsar ◽  
◽  
Artem O. Belovolov ◽  
Keyword(s):  
Hamming Distance ◽  
Suggested Method ◽  
New Method ◽  
Minimization Method ◽  
Polynomial Extension ◽  
Logic Functions ◽  
Logical Functions

A new minimization method of logic functions of n variables in polynomial set-theoretical format has been considered. The method based on the so-called “handshaking” procedure. This procedure reflects the iterative polynomial extension of two conjuncterms of different ranks, the Hamming distance between which can be arbitrary. The advantages of the suggested method are illustrated by the examples.

scholarly journals Regular Matroids Have Polynomial Extension Complexity

2021 ◽  
Author(s):  
Manuel Aprile ◽  
Samuel Fiorini
Keyword(s):  
Spanning Tree ◽  
Extended Formulations ◽  
Polynomial Extension ◽  
Regular Matroid ◽  
Extension Complexity ◽  
Special Case

We prove that the extension complexity of the independence polytope of every regular matroid on [Formula: see text] elements is [Formula: see text]. Past results of Wong and Martin on extended formulations of the spanning tree polytope of a graph imply a [Formula: see text] bound for the special case of (co)graphic matroids. However, the case of a general regular matroid was open, despite recent attempts. We also consider the extension complexity of circuit dominants of regular matroids, for which we give a [Formula: see text] bound.

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