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Vietnam Journal of Mathematics 37:4 (2009) 527-535  

Rings over which Polynomial Rings are Semi-commutative

Yang Gang and Du Ruijuan

Abstract.  We introduce SSC rings and show that these rings and reversible rings are independent subclasses of the class of semi-commutative rings. We develop their basic properties: this class is closed under subdirect products, polynomial extensions, Laurent polynomial extensions. We also provide construction techniques and examples of SSC rings. At last, we obtain that R is right (resp. left) strongly Hopfian if and only if the polynomial factor ring R[x]/(xⁿ⁺¹) is right (resp. left) strongly Hopfian, where (xⁿ⁺¹) is the ideal generated by xⁿ⁺¹ and n is any nonnegative number, in case the ring R satisfies the property (P)$.

2000 Mathematics Subject Classification: 16N60, 16P60.

Keywords: Reduced ring, reversible ring, semi-commutative ring, SSC ring, strongly Hopfian.

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Published by Springer since January 2013