  In this paper, by using Gr\"obner-Shirshov bases, we show that in the
following classes, each (resp. countably generated) algebra can be embedded
into a simple (resp. two-generated) algebra: associative differential algebras,
associative $\Omega$-algebras, associative $\lambda$-differential algebras. We
show that in the following classes, each countably generated algebra over a
countable field $k$ can be embedded into a simple two-generated algebra:
associative algebras, semigroups, Lie algebras, associative differential
algebras, associative $\Omega$-algebras, associative $\lambda$-differential
algebras. Also we prove that any countably generated module over a free
associative algebra $k< X>$ can be embedded into a cyclic $k< X>$-module, where
$|X|>1$. We give another proofs of the well known theorems: each countably
generated group (resp. associative algebra, semigroup, Lie algebra) can be
embedded into a two-generated group (resp. associative algebra, semigroup, Lie
algebra).
