An ideal I is primal over a commutative ring R with non zero identity if the set of all elements
that are not prime to I, forms an ideal of R. This definition was introduced by Ladislas Fuchs …

α1 , α2 Near-Rings 1 Introduction Page 1 International Journal of Algebra, Vol. 4, 2010, no. 2,
71 - 79 α1 , α2 Near-Rings S. Uma Department of Mathematics Kumaraguru College of …

It has been proved that, if R is a near-ring with no non-zero nilpotent two-sided R-subsets
and if the annihilator of any non-zero ideal is contained in some maximal annihilator, then R …

In this paper, D-strong and almost D-strong near-rings have been defined. It has been
proved that if R is a D-strong S-near ring, then prime ideals, strictly prime ideals and …

In [I] the concept of strongly prime near-rings were introduced. In this note we show that
some of the results which were proved for zero-symmetric near-rings are also valid for …

In this paper, we introduce the concept of weakly primary ideals over non-commutative rings.
Several results on weakly primary ideals over non-commutative rings are proved. We prove …

Let R be any ring; a∈ R is called a weak zero-divisor if there are r, s∈ R with ras= 0 and rs=
0. It is shown that, in any ring R, the elements of a minimal prime ideal are weak zero …

Introduction: All rings in this paper are associative and have an identity. All modules will be
daitary. Let R be any ring and M a left R-module. A submodule N of M is called essential if …