The k-Derivation of a Gamma-Ring

Hatice KANDAMAR

Makale detayları

The k-Derivation of a Gamma-Ring

Yazarlar:

Hatice KANDAMAR

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2000 Vol.24 Issue 3, pp.221-231

Belge Tipi:

Makale

Yayın Tarihi:

2/2000

Belge Dili:

Türkçe

Document ID (Org No.):

2000749169

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

In this paper, the k-derivation is defined on a G-ring M (that is, if M is a G-ring, d:M\to M and k:G\to G are to additive maps such that d(ab b )= d(a)b b + ak(b)b + ab d(b)  for all   a,b\in M, \quad b \in G, then d is called a k-derivation of M) and the following results are proved.  (1)  Let R be a ring of characteristic not equal to 2 such that if xry=0 for all x, y\in R then r=0. If d is a k-derivation of the (R=)G-ring R with k=d, then d is the ordinary derivation of R. (2) Let M be a nonzero prime G-ring of characteristic not equal to 2, g be an element of G and a is an element in M such that [ [x, a]g , a]g =0 for all x\in M. Then ag a = 0 or a\in Cg. (3) Let M be a prime G-ring with CharM \ne 2, d be a nonzero k-derivation of M, g be a nonzero element of G and k(g) \ne 0. If d(M) \subseteq Cg, then M is a commutative G-ring.

 

In this paper, the k-derivation is defined on a G-ring M (that is, if M is a G-ring, d:M\to M and k:G\to G are to additive maps such that d(ab b )= d(a)b b + ak(b)b + ab d(b)  for all   a,b\in M, \quad b \in G, then d is called a k-derivation of M) and the following results are proved.  (1)  Let R be a ring of characteristic not equal to 2 such that if xry=0 for all x, y\in R then r=0. If d is a k-derivation of the (R=)G-ring R with k=d, then d is the ordinary derivation of R. (2) Let M be a nonzero prime G-ring of characteristic not equal to 2, g be an element of G and a is an element in M such that [ [x, a]g , a]g =0 for all x\in M. Then ag a = 0 or a\in Cg. (3) Let M be a prime G-ring with CharM \ne 2, d be a nonzero k-derivation of M, g be a nonzero element of G and k(g) \ne 0. If d(M) \subseteq Cg, then M is a commutative G-ring.

Makale detayları

The k-Derivation of a Gamma-Ring

Yazarlar:

Hatice KANDAMAR

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2000 Vol.24 Issue 3, pp.221-231

Belge Tipi:

Makale

Yayın Tarihi:

2/2000

Belge Dili:

Türkçe

Document ID (Org No.):

2000749169

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

k-derivation

derivation

commutativity

gamma-ring.

Sayı

Makale detayları

The k-Derivation of a Gamma-Ring

Yazarlar: Hatice KANDAMAR

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2000 Vol.24 Issue 3, pp.221-231

Belge Tipi: Makale

Yayın Tarihi: 2/2000

Belge Dili: Türkçe

Document ID (Org No.): 2000749169

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

k-derivation

derivation

commutativity

gamma-ring.

Sayı

Yazarlar:

Hatice KANDAMAR

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2000 Vol.24 Issue 3, pp.221-231

Belge Tipi:

Makale

Yayın Tarihi:

2/2000

Belge Dili:

Türkçe

Document ID (Org No.):

2000749169

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098