Radicals of Regular Near Rings.
Rank and perimeter preserver of rank-1 matrices over max algebra
For a rank-1 matrix over max algebra, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over max algebra. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices if and only if it has the form T(A) = U ⊗ A ⊗ V, or with some monomial matrices U and V.
Rational semimodules over the max-plus semiring and geometric approach to discrete event systems
We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete event systems. We say that a subsemimodule of the free semimodule over a semiring is rational if it has a generating family that is a rational subset of , being thought of as a monoid under the entrywise product. We show that for various semirings of max-plus type whose elements are integers, rational semimodules...
Recent results in hyperring and hyperfield theory.
Reduced near-rings
Reduction Theorems for Endomorphism Near-Rings.
Regular additively inverse semirings.
Regular semirings.
Residual quotient fuzzy subset in near-rings.
Ringe mit nichtkommutativer Addition I.
Ring-like operations is pseudocomplemented semilattices
Ring-like operations are introduced in pseudocomplemented semilattices in such a way that in the case of Boolean pseudocomplemented semilattices one obtains the corresponding Boolean ring operations. Properties of these ring-like operations are derived and a characterization of Boolean pseudocomplemented semilattices in terms of these operations is given. Finally, ideals in the ring-like structures are defined and characterized.
Rough semigroups and rough fuzzy semigroups based on fuzzy ideals
In this paper, we firstly introduce a special congruence relation U(μ, t) induced by a fuzzy ideal μ in a semigroup S. Then we define the lower and upper approximations based on a fuzzy ideal in semigroups. We can establish rough semigroups, rough ideals, rough prime ideals, rough fuzzy semigroups, rough fuzzy ideals and rough fuzzy prime ideals according to the definitions of rough sets and rough fuzzy sets. Furthermore, we shall consider the relationships among semigroups and rough semigroups,...