Biswas, On fuzzy semiprime
ideals of a semiring, The Journal of Fuzzy Mathematics, 8(3), (2000).
Among their topics are chains in semiprime
and prime ideals in Leavitt path algebras, a category of extensions with endomorphism rings that have at most four maximal ideals, modules invariant under monomorphisms of their envelopes, rings in which every unit is a sum of a nilpotent and an idempotent, and direct sums of completely almost self-injective modules.` ([umlaut] Ringgold, Inc., Portland, OR)
"Even if Moore's Law continued at its pace, by 2040 it would still take a billion years to factor RSA-2018," a 2,048-bit 617-digit semiprime
Khan, and Faizullah, "Semiprime
([member of], [member of] V[q.sub.k]-fuzzy ideals in ordered semigroups," World Applied Sciences Journal, vol.
 introduced the new notion of prime and semiprime
Zalar () generalized the result to 2-torsion free semiprime
rings as follows: if R is a 2-torsion free semiprime
ring and [phi] is an additive mapping on R such that [phi]([A.sub.2]) = [phi](A)A (resp., [phi]([A.sub.2]) = A[phi](A)) for any A [member of] R, then 0 is a left (resp., a right) centralizer.
In Section 3, we have introduced "generalized rough fuzzy ideal" and "generalized rough fuzzy prime (semiprime
, primary) ideals" of quantales and give a few properties of such ideals.
A sufficient condition to assure the associativity is to require that the algebra A, on which the group acts partially, is semiprime
, that is, all its non zero ideals are either idempotent or nondegenerate.
Martindale, III, Centralizing mappings of semiprime
rings with differential identities," Bulletin of the Institute of Mathematics.
Motivated by the concept of semiprime
ideals studied by Rav in , Zhao in  first introduced the concept of semicontinuous lattices and showed that semicontinuous lattices have many properties similar to that of continuous lattices.
Moreover, several authors studied commutativity in prime and semiprime
rings admitting derivations and generalized derivations which satisfy appropriate algebraic conditions on suitable subsets of the rings.