scholarly journals Free subalgebras of quotient rings of Ore extensions

2012 ◽  
Vol 6 (7) ◽  
pp. 1349-1367 ◽  
Author(s):  
Jason Bell ◽  
Daniel Rogalski
Keyword(s):  
Ore Extensions ◽  
Free Subalgebras ◽  
Quotient Rings

Symmetric Martindale Quotient Rings of Ore Extensions with More than One Indeterminate

2015 ◽  
Vol 43 (8) ◽  
pp. 3123-3133
Author(s):  
Chen-Lian Chuang ◽  
Yuan-Tsung Tsai
Keyword(s):  
Ore Extensions ◽  
Quotient Rings

scholarly journals Quotient Rings of Ore Extensions with More than One Indeterminate

2008 ◽  
Vol 36 (10) ◽  
pp. 3608-3615 ◽  
Author(s):  
Yuan-Tsung Tsai ◽  
Chen-Lian Chuang
Keyword(s):  
Ore Extensions ◽  
Quotient Rings

On a ring structure related to annihilators

2016 ◽  
Vol 16 (08) ◽  
pp. 1750156
Author(s):  
Chan Yong Hong ◽  
Chan Huh ◽  
Hong Kee Kim ◽  
Nam Kyun Kim ◽  
Yang Lee ◽  
...  
Keyword(s):  
Ring Structure ◽  
Artinian Rings ◽  
Ore Extensions ◽  
Quotient Rings

In this note, we focus our attention on a new ring structure related to annihilators, and consider a ring property that contains many kinds of ring classes, introducing right ZAFS. This property is shown to be not left-right symmetric but left-right symmetric for left or right Artinian rings. The left (right) ZAFS property is shown to pass to Ore extensions with automorphisms. The left (respectively, right) ZAFS property is shown to pass also to classical left (respectively, right) quotient rings, yielding that semiprime right Goldie rings are ZAFS.

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.

Centers of maximal quotient rings

1988 ◽  
Vol 50 (4) ◽  
pp. 342-347 ◽  
Author(s):  
Pere Ara
Keyword(s):  
Quotient Rings

scholarly journals Quotient rings of Noetherian module finite rings

1994 ◽  
Vol 121 (2) ◽  
pp. 335-335 ◽  
Author(s):  
A. W. Chatters ◽  
C. R. Hajarnavis
Keyword(s):  
Finite Rings ◽  
Noetherian Module ◽  
Quotient Rings

Ore extensions of quasitriangular Hopf group coalgebras

2014 ◽  
Vol 13 (06) ◽  
pp. 1450016 ◽  
Author(s):  
Daowei Lu ◽  
Dingguo Wang
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Baxter Equation ◽  
Ore Extension ◽  
Ore Extensions ◽  
Necessary And Sufficient

In this paper, we mainly consider some special Ore extension of quasitriangular Hopf group coalgebra, and give the necessary and sufficient conditions when the Ore extension of quasitriangular Hopf group coalgebras will preserve the same quasitriangular structure. Furthermore, in the two examples given at the end, we construct new solutions of Yang–Baxter equation of Hopf group coalgebras version.

ANNIHILATOR CONDITIONS IN MATRIX AND SKEW POLYNOMIAL RINGS

2012 ◽  
Vol 11 (04) ◽  
pp. 1250079 ◽  
Author(s):  
A. ALHEVAZ ◽  
A. MOUSSAVI
Keyword(s):  
Polynomial Rings ◽  
Trivial Extension ◽  
Skew Polynomial Ring ◽  
Matrix Rings ◽  
Skew Polynomial Rings ◽  
Armendariz Rings ◽  
Ore Extensions ◽  
Necessary And Sufficient ◽  
Skew Polynomial ◽  
Armendariz Ring

Let R be a ring with an endomorphism α and α-derivation δ. By [A. R. Nasr-Isfahani and A. Moussavi, Ore extensions of skew Armendariz rings, Comm. Algebra 36(2) (2008) 508–522], a ring R is called a skew Armendariz ring, if for polynomials f(x) = a0 + a1 x + ⋯ + anxn, g(x) = b0+b1x + ⋯ + bmxm in R[x; α, δ], f(x)g(x) = 0 implies a0bj = 0 for each 0 ≤ j ≤ m. In this paper, radicals of the skew polynomial ring R[x; α, δ], in terms of a skew Armendariz ring R, is determined. We prove that several properties transfer between R and R[x; α, δ], in case R is an α-compatible skew Armendariz ring. We also identify some "relatively maximal" skew Armendariz subrings of matrix rings, and obtain a necessary and sufficient condition for a trivial extension to be skew Armendariz. Consequently, new families of non-reduced skew Armendariz rings are presented and several known results related to Armendariz rings and skew polynomial rings will be extended and unified.

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