Primeness in near-rings of continuous maps

• Main Author: Mogae, Kabelo
• Format: Others
• Language: English
• Published: Nelson Mandela Metropolitan University
• Subjects: Near-rings; Topological algebras
• Online Access: http://hdl.handle.net/10948/d1020597

The prototype of a near-ring is the set of all self-maps of an additively written (but not necessarily abelian) group under pointwise addition and composition of maps. Moreover, any near-ring with unity can be embedded in a near-ring (with unity) of self-maps of some group. For this reason, a lot of research has been done on near-rings of maps. In 1979, Hofer [16] gave the study of near-rings of maps a topological avour by considering the near- ring of all continuous self-maps of a topological group. In this dissertation we consider some standard constructions of near-rings of maps on a group G and investigate these when G is a topological group and our near-ring consists of continuous maps.