Generalized semicommutative rings and their extensions


BAŞER M., Harmanci A., Kwak T. K.

BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, cilt.45, ss.285-297, 2008 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 45 Konu: 2
  • Basım Tarihi: 2008
  • Doi Numarası: 10.4134/bkms.2008.45.2.285
  • Dergi Adı: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.285-297

Özet

For an endomorphism a of a ring R., the endomorphism a is called semicommutative if ab = 0 implies a Ha(b) = 0 for a is an element of R. A ring R is called alpha-semicommulative if there exists a semicommutative endomorphism a of R. In this paper, various results of semicommutative rings are extended to a-semicommutative rings. In addition, we introduce the notion of an alpha-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 R[[x; alpha]]. We show that a number of interesting properties of a ring R transfer to its the skew power series ring R[[X; alpha]] and vice-versa such as the Baer property and the p.p.-property, when R is a-skew power series Armendariz. Several known results relating to a-rigid rings can be obtained as corollaries of our results.