Partial orders in semigroups and semirings of right quotients.
Plongement d'un groupoïde médian dans le groupoïde multiplicatif d'un semi-anneau médian
Prime ideals in semirings.
Principal element lattices
Properties of fuzzy relations powers
Properties of - compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider - powers of fuzzy relations under diverse assumptions about operation. At first, we remind fundamental properties of - composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations are examined....
Pseudocomplements in sum-ordered partial semirings
We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several...
Pseudoringe
Pseudosemirings induced by ortholattices
Quasitrivial semimodules. I.
Quasitrivial semimodules. II.
Quasitrivial semimodules. III.
Quasitrivial semimodules. IV.
Almost quasitrivial and critical semimodules are studied.
Quasitrivial semimodules. V.
Critical semimodules over congruence-simple semirings are studied.
Quasitrivial semimodules. VI.
The paper continues the investigation of quasitrivial semimodules and related problems. In particular, endomorphisms of semilattices are investigated.
Quasitrivial semimodules. VII.
The paper continues the investigation of quasitrivial semimodules and related problems. In particular, strong endomorphisms of semilattices are studied.
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.
Regular additively inverse semirings.
Regular semirings.