ON COMMUTATIVITY IN PRIME Γ-NEAR-RINGS WITH SYMMETRIC BI-DERIVATIONS
Kalyan Kumar Dey1 §, Akhil Chandra Paul2, Isamiddin S. Ra Page 1 International Journal …

In this paper, we define β-insulator and strongly prime Γ-rings. We also prove that the
following main results:(i) If a Γ-ring M is weakly semiprime then M is strongly prime if and …

The notion of a Γ-ring was first introduced by Nobusawa. The class of Γ-rings contains not
only all rings but also Hestenes ternary rings. Recently, the author proved the following two …

For preliminary definitions and results related to near-rings, we refer to Pilz [11]. The notion
of a Γ-ring, a concept more general than a ring, was defined by Nobusawa [8]. Barnes [1] …

BI-Regular Near-Rings Page 1 Southeast Asian Bulletin of Mathematics cO SEAMS. 2009
Southeast Asian Bulletin of Mathematics (2009) 33: 491–496 BI-Regular Near-Rings P …

Let M be a Γ-ring with right operator ring R. We define one-sided ideals of M and show that
there is a one-to-one correspondence between the prime left ideals of M and R and hence …

The aim of this paper is to generalize the notion of $ z $-ideals to arbitrary noncommutative
rings. A left (right) ideal $ I $ of a ring $ R $ is called a left (right) $ z $-ideal if …

Let M and r be additive abelian groups. If for all a, byc^ M and a, ßj^ r> the conditions (1)
aab^ M, aaß^ T,(2)(a+ b) ac= aac+ bac, a (a+ ßs) b= aab+ aßb, aa (b+ c)= aab+ aac,(a+ ß) …

Let M be a weak Nobusawa Γ-ring and γ be a nonzero element of Γ. In this paper, we find a
relation between Γ-rings and rings, and give some commutativity conditions on Γ-rings by …