On near-rings with two-sided a-derivations

Nurcan ARGAÇ

Makale detayları

On near-rings with two-sided a-derivations

Yazarlar:

Nurcan ARGAÇ

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2004 Vol.28 Issue 2, pp.195-204

Belge Tipi:

Makale

Yayın Tarihi:

1/2004

Belge Dili:

Türkçe

Document ID (Org No.):

2000748786

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

In this paper, we introduce the notion of two-sided  a-derivation of a near-ring and give some generalizations of [1].   Let N be a near ring.  An additive mapping f: N\rightarrow N is called  an { \it (a, b)-derivation } if there exist functions  a,b : N\rightarrow N such that f(xy)=f(x)a(y)+b  (x)f(y) for all x,y\in N. An additive mapping d:N\rightarrow N is  called a two-sided a-derivation if d is an (a,1)-derivation  as well as a (1,a)-derivation.  The purpose of this paper is to  prove the following two assertions: (i) Let N be a semiprime  near-ring, I be a subset of N such that 0\in I, IN\subseteq I and d be  a two-sided a-derivation of N. If d acts as a homomorphism on I  or as an anti-homomorphism on I under certain conditions on a,  then d(I)= {0}.  (ii) Let N be a prime near-ring, I be a nonzero  semigroup ideal of N, and d be a (a, 1)-derivation on N. If d+d  is additive on I, then (N,+) is abelian.

 

In this paper, we introduce the notion of two-sided  a-derivation of a near-ring and give some generalizations of [1].   Let N be a near ring.  An additive mapping f: N\rightarrow N is called  an { \it (a, b)-derivation } if there exist functions  a,b : N\rightarrow N such that f(xy)=f(x)a(y)+b  (x)f(y) for all x,y\in N. An additive mapping d:N\rightarrow N is  called a two-sided a-derivation if d is an (a,1)-derivation  as well as a (1,a)-derivation.  The purpose of this paper is to  prove the following two assertions: (i) Let N be a semiprime  near-ring, I be a subset of N such that 0\in I, IN\subseteq I and d be  a two-sided a-derivation of N. If d acts as a homomorphism on I  or as an anti-homomorphism on I under certain conditions on a,  then d(I)= {0}.  (ii) Let N be a prime near-ring, I be a nonzero  semigroup ideal of N, and d be a (a, 1)-derivation on N. If d+d  is additive on I, then (N,+) is abelian.

Makale detayları

On near-rings with two-sided a-derivations

Yazarlar:

Nurcan ARGAÇ

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2004 Vol.28 Issue 2, pp.195-204

Belge Tipi:

Makale

Yayın Tarihi:

1/2004

Belge Dili:

Türkçe

Document ID (Org No.):

2000748786

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Prime near-ring

semiprime near-ring

(a

1)-derivation

(1

a)-derivation

two-sided a-derivation.

Sayı

Makale detayları

Yazarlar: Nurcan ARGAÇ

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2004 Vol.28 Issue 2, pp.195-204

Belge Tipi: Makale

Yayın Tarihi: 1/2004

Belge Dili: Türkçe

Document ID (Org No.): 2000748786

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Nurcan ARGAÇ

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2004 Vol.28 Issue 2, pp.195-204

Belge Tipi:

Makale

Yayın Tarihi:

1/2004

Belge Dili:

Türkçe

Document ID (Org No.):

2000748786

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098