Generalized Derivations on Prime Near Rings
Let be a near ring. An additive mapping is said to be a
right generalized (resp., left generalized) derivation with associated derivation on if (resp., ) for all . A mapping
 is said to be a generalized derivation with associated derivation on if
 is both a right generalized and a left generalized derivation with associated derivation
 on . The purpose of the present paper is to prove some theorems in the setting of
a semigroup ideal of a 3-prime near ring admitting a generalized derivation, thereby
extending some known results on derivations.
On Derivations in Near-Rings, II
Let N denote a 3–prime zero-symmetric left near-ring, and let d be a nonzero derivation on N. Let U ≠ φ be a nonzero subset of N such that (i) U N ⊆ U or (ii) N U ⊆ U. We prove that N must be a commutative ring if one of the following holds: (a) U satisfies one of (i) and (ii), and d(U) is multiplicatively central; (b) U satisfies both of (i) and (ii), d 2 ≠ 0, and [d(U), d(U)] = {0}. Some related results are also given.
Religion and school
The report presents and argues in favor of the thesis that the secular school offers no alternative in modern society. Simultaneously, the author displays the basic contours of spiritual physiognomy of such a modern school which in many ways differs from the, school we know in this country. The school the author pleads for does not decide among various contents that influence forming of the young, within which the line is established between theism - atheism, but, on the contrary, pleads for the principle of humanistic education. The predominant here is the notion of methodological skepticism which marks the principle by which the process of education should be realized as though there were no God, or - which is on the same level - as though there were God. Out of this basic principle any others upon which the concept of modern secular school the author pleads for is established can be drawn. It ought not to neglect the rich, scientifically confirmed knowledge on the phenomenon of religion and atheism, which should be, presented in all school subjects where the contents allow for it as well as the Religious Culture should be introduced as a compulsory subject. By introducing this subject as a collection of knowledge on the phenomenon of the, religious, we would avoid imposing a particular religious culture as an attitude, behavior, belief and evaluation.