Topological N-Groups Where the Nearrings are Real Nearrings

Abstract

In this paper, nearrings will be right nearrings. Standard references for algebraic nearrings include [2], [5] and [6]. Let N be a topological nearring. A topological N-group is a pair (G, μ) where G is a topological group and μ is a continuous function from N × G into G such that the following two conditions are satisfied for all a, b ∈ N and c ∈ G:

$$\mu (a + b,c) = \mu (a,c) + \mu (b,c)$$

((1A))

,

$$\mu (ab,c) = \mu (a,\mu (b,c))$$

((1B))

.