H-Primes in Iterated Skew Polynomial Algebras

2002 ◽  
pp. 173-183
Author(s):  
Ken A. Brown ◽  
Ken R. Goodearl
Keyword(s):  
Polynomial Algebras ◽  
Skew Polynomial

scholarly journals PBW BASES FOR SOME 3-DIMENSIONAL SKEW POLYNOMIAL ALGEBRAS

2017 ◽  
Vol 101 (6) ◽  
pp. 1207-1228 ◽  
Author(s):  
Armando Reyes ◽  
Héctor Suárez
Keyword(s):  
Polynomial Algebras ◽  
3 Dimensional ◽  
Skew Polynomial

More on Iterated Skew Polynomial Algebras

2002 ◽  
pp. 185-193
Author(s):  
Ken A. Brown ◽  
Ken R. Goodearl
Keyword(s):  
Polynomial Algebras ◽  
Skew Polynomial

scholarly journals Skew polynomial algebras with coefficients in Koszul Artin–Schelter regular algebras

2013 ◽  
Vol 390 ◽  
pp. 231-249 ◽  
Author(s):  
Ji-Wei He ◽  
Fred Van Oystaeyen ◽  
Yinhuo Zhang
Keyword(s):  
Polynomial Algebras ◽  
Regular Algebras ◽  
Skew Polynomial

Free subgroups in k(x 1,... ,x n )(X;σ) and k(x,y)(k;σ)

2019 ◽  
Vol 31 (3) ◽  
pp. 769-777
Author(s):  
Jairo Z. Gonçalves
Keyword(s):  
Normal Subgroup ◽  
Polynomial Ring ◽  
Multiplicative Group ◽  
Free Subgroup ◽  
Laurent Polynomials ◽  
Skew Polynomial Ring ◽  
Ring Of Fractions ◽  
Skew Polynomial ◽  
Free Subgroups ◽  
Mild Restriction

Abstract Let k be a field, let {\mathfrak{A}_{1}} be the k-algebra {k[x_{1}^{\pm 1},\dots,x_{s}^{\pm 1}]} of Laurent polynomials in {x_{1},\dots,x_{s}} , and let {\mathfrak{A}_{2}} be the k-algebra {k[x,y]} of polynomials in the commutative indeterminates x and y. Let {\sigma_{1}} be the monomial k-automorphism of {\mathfrak{A}_{1}} given by {A=(a_{i,j})\in GL_{s}(\mathbb{Z})} and {\sigma_{1}(x_{i})=\prod_{j=1}^{s}x_{j}^{a_{i,j}}} , {1\leq i\leq s} , and let {\sigma_{2}\in{\mathrm{Aut}}_{k}(k[x,y])} . Let {D_{i}} , {1\leq i\leq 2} , be the ring of fractions of the skew polynomial ring {\mathfrak{A}_{i}[X;\sigma_{i}]} , and let {D_{i}^{\bullet}} be its multiplicative group. Under a mild restriction for {D_{1}} , and in general for {D_{2}} , we show that {D_{i}^{\bullet}} , {1\leq i\leq 2} , contains a free subgroup. If {i=1} and {s=2} , we show that a noncentral normal subgroup N of {D_{1}^{\bullet}} contains a free subgroup.

scholarly journals PI degree parity in q-skew polynomial rings

2008 ◽  
Vol 319 (10) ◽  
pp. 4199-4221 ◽  
Author(s):  
Heidi Haynal
Keyword(s):  
Polynomial Rings ◽  
Skew Polynomial Rings ◽  
Skew Polynomial

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.

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