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http://dx.doi.org/10.4134/BKMS.2012.49.2.381

INSERTION-OF-FACTORS-PROPERTY ON NILPOTENT ELEMENTS  

Baek, Jin-Eon (Department of Mathematics Korea Science Academy of KAIST)
Chin, Woo-Young (Department of Mathematics Korea Science Academy of KAIST)
Choi, Ji-Woong (Department of Mathematics Korea Science Academy of KAIST)
Eom, Tae-Hyun (Department of Mathematics Korea Science Academy of KAIST)
Jeon, Young-Cheol (Department of Mathematics Korea Science Academy of KAIST)
Lee, Yang (Department of Mathematics Pusan National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.2, 2012 , pp. 381-394 More about this Journal
Abstract
We generalize the insertion-of-factors-property by setting nilpotent products of elements. In the process we introduce the concept of a nil-IFP ring that is also a generalization of an NI ring. It is shown that if K$\ddot{o}$the's conjecture holds, then every nil-IFP ring is NI. The class of minimal noncommutative nil-IFP rings is completely determined, up to isomorphism, where the minimal means having smallest cardinality.
Keywords
nilpotent element; IFP ring; nil-IFP ring; NI ring; polynomial ring;
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