Division hypernear-rings

T-fuzzy Subhypernear-rings of Hypernear-rings

Using a t-norm T , the notion of T -fuzzy subhypernear-rings (for short TFSrings) of hypernear-rings is introduced and some of their properties are investigated. Also we study the structure of TFS-rings under direct product.

On Intuitionistic Fuzzy Subhypernear-rings of Hypernear-Rings

In this paper, we introduce the concept of an intuitionistic fuzzy subhypernearring of a hypernear-ring and obtain some results in this connection.

Triangulaizability of Algebras Over Division Rings

Planar Division Neo-rings

Introduction. The notion of a division ring can be generalized to give a system whose addition is not necessarily associative, but which retains the property of coordinatizing an affine plane. Such a system will be called a planar division neo-ring (PDNR); examples of (infinite) PDNRs which are not division rings are known. If (R, +, •) is a finite power-associative PDNR, then (R, +) is shown t...

Stable division rings

It is shown that a stable division ring with positive characteristic has finite dimension over its centre. This is then extended to simple division rings. Macintyre proved any ω-stable field to be either finite or algebraically closed [7]. This was generalised by Cherlin and Shelah to superstable fields [3]. It follows that a superstable division ring is a field [2]. The result was broadened to...