Primitivity of skew polynomial and skew laurent polynomial rings

1996 ◽  
Vol 24 (7) ◽  
pp. 2271-2284 ◽  
Author(s):  
André Leroy ◽  
Jerzy Matczuk
Keyword(s):  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Skew Polynomial

Radicals in skew polynomial and skew Laurent polynomial rings

2014 ◽  
Vol 218 (10) ◽  
pp. 1916-1931 ◽  
Author(s):  
Chan Yong Hong ◽  
Nam Kyun Kim ◽  
Pace P. Nielsen
Keyword(s):  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Skew Polynomial

A GENERALIZATION OF NIL-ARMENDARIZ RINGS

2013 ◽  
Vol 12 (06) ◽  
pp. 1350001 ◽  
Author(s):  
MOHAMMAD HABIBI ◽  
RAOUFEH MANAVIYAT
Keyword(s):  
Sufficient Conditions ◽  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Monoid Ring ◽  
Skew Polynomial Rings ◽  
Monoid Homomorphism ◽  
Special Cases ◽  
Armendariz Rings ◽  
Skew Polynomial ◽  
The Relationship

Let R be a ring, M a monoid and ω : M → End (R) a monoid homomorphism. The skew monoid ring R * M is a common generalization of polynomial rings, skew polynomial rings, (skew) Laurent polynomial rings and monoid rings. In the current work, we study the nil skew M-Armendariz condition on R, a generalization of the standard nil-Armendariz condition from polynomials to skew monoid rings. We resolve the structure of nil skew M-Armendariz rings and obtain various necessary or sufficient conditions for a ring to be nil skew M-Armendariz, unifying and generalizing a number of known nil Armendariz-like conditions in the aforementioned special cases. We consider central idempotents which are invariant under a monoid endomorphism of nil skew M-Armendariz rings and classify how the nil skew M-Armendariz rings behaves under various ring extensions. We also provide rich classes of skew monoid rings which satisfy in a condition nil (R * M) = nil (R) * M. Moreover, we study on the relationship between the zip and weak zip properties of a ring R and those of the skew monoid ring R * M.

scholarly journals Radicals of skew polynomial rings and skew Laurent polynomial rings

2011 ◽  
Vol 331 (1) ◽  
pp. 428-448 ◽  
Author(s):  
Chan Yong Hong ◽  
Nam Kyun Kim ◽  
Yang Lee
Keyword(s):  
Laurent Polynomial ◽  
Polynomial Rings ◽  
Skew Polynomial Rings ◽  
Skew Polynomial

Partial Skew Polynomial Rings Over Semisimple Artinian Rings

2010 ◽  
Vol 38 (5) ◽  
pp. 1663-1676 ◽  
Author(s):  
Wagner Cortes ◽  
Miguel Ferrero ◽  
Yasuyuki Hirano ◽  
Hidetoshi Marubayashi
Keyword(s):  
Polynomial Rings ◽  
Artinian Rings ◽  
Skew Polynomial Rings ◽  
Skew Polynomial
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