Faithful f-Free Algebras

Kosan M. T. , Lee T., Zhou Y.

COMMUNICATIONS IN ALGEBRA, cilt.41, sa.2, ss.638-647, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 41 Konu: 2
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1080/00927872.2011.632798
  • Sayfa Sayıları: ss.638-647


For a polynomial with zero constant term, a semiprime K-algebra R is called faithful f-free if every nonzero ideal of R does not satisfy f. We prove that a semiprime algebra has an essential ideal which is the direct sum of its largest faithful f-free ideal and its largest ideal satisfying the identity f. Here, faithful f-free algebras are characterized, and applications to some interesting differential identities are discussed. Especially with f=S2n (n1), a description of semiprime rings is obtained in terms of faithful S2n-free rings and semiprime PI-rings of degree 2n. Semiprime PI-rings of degree 2n are realized through faithful S2n-rings. Finally, faithful S2n-rings are characterized.