BOOLEAN LIKE NEAR RINGS

摘要

The concepts of Boolean like near-ring and special boolean like ring are introduced. It is shown that these two concepts are equivalent. An example of a Boolean like near ring which is not a Boolean like ring is furnished. It is also shown that a special boolean like ring with identity is a boolean like ring and conversly. It is proved that the set Ⅰ of all nilpotent elements in a boolean like near-ring N is an ideal and N/I is a boolean ring. Finally it is proved that a proper ideal in a special boolean-like ring R with R~2 = R is maximal if and only if it is prime. In addition, some interesting results are proved.