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GENERALIZED SEMI COMMUTATIVE RINGS AND THEIR EXTENSIONS
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 Title & Authors
GENERALIZED SEMI COMMUTATIVE RINGS AND THEIR EXTENSIONS
Baser, Muhittin; Harmanci, Abdullah; Kwak, Tai-Keun;
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 Abstract
For an endomorphism of a ring R, the endomorphism is called semicommutative if ab=0 implies =0 for a R. A ring R is called -semicommutative if there exists a semicommutative endomorphism of R. In this paper, various results of semicommutative rings are extended to -semicommutative rings. In addition, we introduce the notion of an -skew power series Armendariz ring which is an extension of Armendariz property in a ring R by considering the polynomials in the skew power series ring . We show that a number of interesting properties of a ring R transfer to its the skew power series ring and vice-versa such as the Baer property and the p.p.-property, when R is -skew power series Armendariz. Several known results relating to -rigid rings can be obtained as corollaries of our results.
 Keywords
semicommutative rings;rigid rings;skew power series rings;extended Armendariz rings;Baer rings;p.p.-rings;
 Language
English
 Cited by
1.
ON QUASI-RIGID IDEALS AND RINGS,;;;

대한수학회보, 2010. vol.47. 2, pp.385-399 crossref(new window)
2.
QUASI-ARMENDARIZ PROPERTY FOR SKEW POLYNOMIAL RINGS,;;

대한수학회논문집, 2011. vol.26. 4, pp.557-573 crossref(new window)
3.
STRUCTURE OF ZERO-DIVISORS IN SKEW POWER SERIES RINGS,;;;

대한수학회지, 2015. vol.52. 4, pp.663-683 crossref(new window)
4.
INSERTION-OF-FACTORS-PROPERTY ON SKEW POLYNOMIAL RINGS,;;;;;

대한수학회지, 2015. vol.52. 6, pp.1161-1178 crossref(new window)
1.
ON QUASI-RIGID IDEALS AND RINGS, Bulletin of the Korean Mathematical Society, 2010, 47, 2, 385  crossref(new windwow)
2.
Generalized Semicommutative and Skew Armendariz Ideals, Ukrainian Mathematical Journal, 2015, 66, 9, 1354  crossref(new windwow)
3.
Zero commutativity of nilpotent elements skewed by ring endomorphisms, Communications in Algebra, 2017, 45, 11, 4881  crossref(new windwow)
4.
Zero Divisors in Skew Power Series Rings, Communications in Algebra, 2015, 43, 10, 4427  crossref(new windwow)
5.
STRUCTURE OF ZERO-DIVISORS IN SKEW POWER SERIES RINGS, Journal of the Korean Mathematical Society, 2015, 52, 4, 663  crossref(new windwow)
6.
QUASI-ARMENDARIZ PROPERTY FOR SKEW POLYNOMIAL RINGS, Communications of the Korean Mathematical Society, 2011, 26, 4, 557  crossref(new windwow)
7.
INSERTION-OF-FACTORS-PROPERTY ON SKEW POLYNOMIAL RINGS, Journal of the Korean Mathematical Society, 2015, 52, 6, 1161  crossref(new windwow)
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