scholarly journals Elimination of Variables in Linear Solvable Polynomial Algebras and ∂-Holonomicity

2000 ◽  
Vol 234 (1) ◽  
pp. 101-127 ◽  
Author(s):  
Li Huishi ◽  
Freddy Van Oystaeyen
Keyword(s):  
Polynomial Algebras ◽  
Elimination Of Variables

Families of quasigroup operations satisfying the generalized distributive law

2020 ◽  
Vol 30 (3) ◽  
pp. 187-202
Author(s):  
Sergey V. Polin
Keyword(s):  
System Of Equations ◽  
Systems Of Equations ◽  
The Family ◽  
Distributive Law ◽  
Elimination Of Variables

AbstractThe previous paper was concerned with systems of equations over a certain family 𝓢 of quasigroups. In that work a method of elimination of an outermost variable from the system of equations was suggested and it was shown that further elimination of variables requires that the family 𝓢 of quasigroups satisfy the generalized distributive law (GDL). In this paper we describe families 𝓢 that satisfy GDL. The results are applied to construct classes of easily solvable systems of equations.

scholarly journals Gelfand-Kirillov Dimensions of Modules over Differential Difference Algebras

2016 ◽  
Vol 23 (04) ◽  
pp. 701-720 ◽  
Author(s):  
Xiangui Zhao ◽  
Yang Zhang
Keyword(s):  
Computational Method ◽  
Finitely Generated ◽  
Finitely Generated Module ◽  
Polynomial Algebras ◽  
Ore Extensions ◽  
Basis Method ◽  
Finitely Generated Modules ◽  
Kirillov Dimension

Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension of a finitely generated module over a differential difference algebra through a computational method: Gröbner-Shirshov basis method. We develop the Gröbner-Shirshov basis theory of differential difference algebras, and of finitely generated modules over differential difference algebras, respectively. Then, via Gröbner-Shirshov bases, we give algorithms for computing the Gelfand-Kirillov dimensions of cyclic modules and finitely generated modules over differential difference algebras.

A Note on Geometric Factoriality

1995 ◽  
Vol 38 (4) ◽  
pp. 390-395 ◽  
Author(s):  
S. M. Bhatwadekar ◽  
K. P. Russell
Keyword(s):  
Finite Groups ◽  
Positive Answer ◽  
Integral Representations ◽  
Perfect Field ◽  
Polynomial Algebras ◽  
Representations Of Finite Groups ◽  
Smooth Affine

AbstractLet k: be a perfect field such that is solvable over k. We show that a smooth, affine, factorial surface birationally dominated by affine 2-space is geometrically factorial and hence isomorphic to . The result is useful in the study of subalgebras of polynomial algebras. The condition of solvability would be unnecessary if a question we pose on integral representations of finite groups has a positive answer.

FIXED ELEMENTS OF NONINJECTIVE ENDOMORPHISMS OF POLYNOMIAL ALGEBRAS IN TWO VARIABLES

2016 ◽  
Vol 95 (2) ◽  
pp. 209-213
Author(s):  
YUEYUE LI ◽  
JIE-TAI YU
Keyword(s):  
Associative Algebra ◽  
Characteristic Zero ◽  
Polynomial Algebra ◽  
Free Associative Algebra ◽  
Polynomial Algebras ◽  
Fixed Element ◽  
The Given

Let $A_{2}$ be a free associative algebra or polynomial algebra of rank two over a field of characteristic zero. The main results of this paper are the classification of noninjective endomorphisms of $A_{2}$ and an algorithm to determine whether a given noninjective endomorphism of $A_{2}$ has a nontrivial fixed element for a polynomial algebra. The algorithm for a free associative algebra of rank two is valid whenever an element is given and the subalgebra generated by this element contains the image of the given noninjective endomorphism.

scholarly journals Squaring operations on truncated polynomial algebras

1969 ◽  
Vol 38 (0) ◽  
pp. 39-50 ◽  
Author(s):  
Tamio SUGAWARA ◽  
Hirosi TODA
Keyword(s):  
Polynomial Algebras
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