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ON QUASI-RIGID IDEALS AND RINGS
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 Title & Authors
ON QUASI-RIGID IDEALS AND RINGS
Hong, Chan-Yong; Kim, Nam-Kyun; Kwak, Tai-Keun;
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 Abstract
Let be an endomorphism and I a -ideal of a ring R. Pearson and Stephenson called I a -semiprime ideal if whenever A is an ideal of R and m is an integer such that for all , then , where is an automorphism, and Hong et al. called I a -rigid ideal if implies a for . Notice that R is called a -semiprime ring (resp., a -rigid ring) if the zero ideal of R is a -semiprime ideal (resp., a -rigid ideal). Every -rigid ideal is a -semiprime ideal for an automorphism , but the converse does not hold, in general. We, in this paper, introduce the quasi -rigidness of ideals and rings for an automorphism which is in between the -rigidness and the -semiprimeness, and study their related properties. A number of connections between the quasi -rigidness of a ring R and one of the Ore extension of R are also investigated. In particular, R is a (principally) quasi-Baer ring if and only if is a (principally) quasi-Baer ring, when R is a quasi -rigid ring.
 Keywords
endomorphism;rigidness;semiprimeness;Ore extension;(principally) quasi-Baer ring;
 Language
English
 Cited by
1.
QUASI-ARMENDARIZ PROPERTY FOR SKEW POLYNOMIAL RINGS,;;

대한수학회논문집, 2011. vol.26. 4, pp.557-573 crossref(new window)
1.
QUASI-ARMENDARIZ PROPERTY FOR SKEW POLYNOMIAL RINGS, Communications of the Korean Mathematical Society, 2011, 26, 4, 557  crossref(new windwow)
2.
Special properties of the ring Sn(R), Journal of Algebra and Its Applications, 2016, 1750212  crossref(new windwow)
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