… that the class of prime essential rings is closed under many familiar operations; for example,
polynomial rings and matrix rings over prime essential rings are prime essential. Also, if G is …

… We construct a ring that is right strongly prime but not left strongly prime. … an essential right
R-submodule of S. With these definitions, every ring of quotients is an essential extension ring. …

… We emphasize the injectivity of r in this definition, for it is essential in the construction of the
space-preserving functor from J to 38. We now construct this functor. Let / be a given object of …

… rings to be left V-rings are given. Next, a prime ring with a reduced maximal or essential left
… A prime regular or left v-ring is either primitive or a ring with zero socle such that every non-…

… generates a special atom or contains a nonzero ∗-ring. In this paper, we construct a prime
essential ring R such that lR … Prime essential rings cannot be ∗-rings since the latter must be …

… We study rings in which OP is an essential ideal, whenever P is an essential prime ideal. We
… We prove that the classical ring of quotients of any ring of this kind is itself of this kind. We …

… prime essential rings have an important role in radical theory of rings, we describe some
properties of prime essential rings as … every prime essential rings is a subdirectly reducible ring. …

… (i) Every ideal of a prime essential ring is a prime essential ring. (ii) If I is an essential
ideal of R and I is a prime esssential ring then R is a prime essential ring. … We shall show …

… We recall that I is an essential ideal in N if I a N and I n K # 0 for all 0 # K 4 N and the class
M of near rings is closed under essential extensions if I is an essential ideal of N and I ~ M , …

… is a prime ring and S is its symmetric ring of … ring. Roughly speaking we are given V ;2 R
;2 K where K is a field, R is a K-algebra and V is a left K-vector space. In addition, V is a Lie ring …