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Right Nucleus in Right Alternative Algebras
Author(s) -
Nam Ng Seong
Publication year - 1980
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-21.3.456
Subject(s) - nilpotent , mathematics , semiprime , finitely generated abelian group , pure mathematics , ideal (ethics) , nucleus , torsion (gastropod) , combinatorics , prime (order theory) , law , political science , biology , zoology , microbiology and biotechnology
Suppose that R is a right alternative algebra free of 2 torsion, with right nucleus M . nucleus N . and center C . If R is semiprime and purely nonassociative, then N = C . If further R is finitely generated or free of locally nilpotent ideals, then M = C . If R is prime and M ≠ C , then the associator ideal of R is locally nilpotent.