A bounded linear operator T on a complex Hilbert space H is irreducible if it has no reducing subspace other than the trivial ones (0) and H; it is strongly irreducible if every operator similar to T is irreducible. Equivalently, T is irreducible (resp. strongly irreducible) if the only projections (resp. idempotent operators) commuting with T are 0 and I. Since (strongly) irreducible operators...

An ideal of a ring is completely irreducible if it is not the intersection of any set of proper overideals. We investigate the structure of completely irrreducible ideals in a commutative ring without finiteness conditions. It is known that every ideal of a ring is an intersection of completely irreducible ideals. We characterize in several ways those ideals that admit a representation as an ir...

notions of strongly regular, regular and left(right) regular $gamma$−semigroupsare introduced. equivalent conditions are obtained through fuzzy notion for a$gamma$−semigroup to be either strongly regular or regular or left regular.

We study the local geometry of irreducible parabolic geometries admitting strongly essential flows; these are flows by local automorphisms with higher-order fixed points. We prove several new rigidity results, and recover some old ones for projective and conformal structures, which show that in many cases the existence of a strongly essential flow implies local flatness of the geometry on an op...

Let S be a Heegaard splitting surface of a compact orientable 3-manifold M. If S is strongly irreducible, the manner in which it can intersect a ball or a solid torus in M is very constrained and the allowable configurations are simple and useful. Splitting surfaces not conforming to these simple local pictures must be weakly reducible.

We introduce the notion of reset left regular decomposition of an ideal regular language and we prove that there is a one-to-one correspondence between these decompositions and strongly connected synchronizing automata. We show that each ideal regular language has at least a reset left regular decomposition. As a consequence each ideal regular language is the set of synchronizing words of some ...

The concepts of a prime ideal of a distributively generated (d.g.) nearring R, a prime d.g. near-ring and an irreducible R-group are introduced1). The annihilating ideal of an irreducible R-group with an R-generator is a prime ideal. Consequently we define a prime ideal to be primitively prime if it is the annihilating ideal of such an R-group, and a d.g. near-ring to be a primitively prime nea...