On uniformly strongly prime Γ-semirings (II)
The Uniformly strongly prime k-radical of a Γ-semiring is a special class which we study via its operator semiring.
On unital extensions of near-rings and their radicals.
On valuations of nearfields
On weakly -subcommutative near-rings.
On well-ordered groups and near-rings
On zero-symmetric nearrings with identity whose additive groups are simple
We investigate conditions on an infinite simple group in order to construct a zero-symmetric nearring with identity on it. Using the Higman-Neumann-Neumann extensions and Clay’s characterization, we obtain zero-symmetric nearrings with identity with the additive groups infinite simple groups. We also show that no zero-symmetric nearring with identity can have the symmetric group as its additive group.
One-sided complements and solutions of the equation in semirings.
One-sided -ideals and -ideals in semirings.
Operators , and in the classes of -semigroups and -semirings.
Orderings on semirings.
Orthorings
Certain ring-like structures, so-called orthorings, are introduced which are in a natural one-to-one correspondence with lattices with 0 every principal ideal of which is an ortholattice. This correspondence generalizes the well-known bijection between Boolean rings and Boolean algebras. It turns out that orthorings have nice congruence and ideal properties.