Abstract
In the present paper we shall investigate some decomposition theorems for near rings satisfying any one of the conditions; (1) (2)whereare integers.
Highlights
Throughout, R is a left near ring with multiplicative center Z
A near ring R is said to be distributively generated (d-g) if it contains a multiplicative subsemigroup of distributive elements which generates the additive group (R, +)
Let R be a zero-symmetric near ring satisfying either of the conditions (P1) and (P2)
Summary
Throughout, R is a left near ring with multiplicative center Z. An element x R is said to be distributive if (y + z) x = yx + zx for all y, z R. A near ring R is said to be distributively generated (d-g) if it contains a multiplicative subsemigroup of distributive elements which generates the additive group (R , +). A near ring R is called periodic if for every x R there exist distinct positive integers m = m(x), n = n(x) such that xm = xn. A near ring R is called zero- commutative if xy = 0 implies yx = 0 for all x, y R and if for all x R, 0x = 0 ,. R is called zero-symmetric (recall that left distributivity in R yields x0 = 0)
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