Abstract
A near-ring is a triple (R, +, · such that (R, +) is a group, (R, ·) is a semigroup, and is left distributive work on near-rings is [1]. A near-ring R is distributively generated if there exists S ⊂ R such that (S, ·) is sub-semigroup of (R, ·), each element of S is right distributive, and S is an additive generating set for (R, +). Distributively generated near-rings, first treated in [3], arise out of consideration of the system generated by the endomorphisms of an (not necessarily commutative) additive group. A near-field is a near-ring such that the nozero elements form a group under multiplication. Near fields are discussed in [9]. An element x ≠ 0 in R is a left (right) zero divisor if there is a ≠ 0 in R such that xa = 0 (ax = 0). A zero divisor is an element that is either a left or a right zero divisor. In a near-ring R it will be assumed that Ox = 0 for each x ∈ R.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
