Ordered ultraconnected rings
Order-enriched solid functors
Order-enriched solid functors, as presented in this paper in two versions, enjoy many of the strong properties of their ordinary counterparts, including the transfer of the existence of weighted (co)limits from their codomains to their domains. The ordinary version of the notion first appeared in Trnková's work on automata theory of the 1970s and was subsequently studied by others under various names, before being put into a general enriched context by C. Anghel. Our focus in this paper is on differentiating...
Ordering of observables and characterization of conditional expectation
Ordering the set of antichains of an ordered set.
Orderings and preorderings in rings with involution
The notions of a preordering and an ordering of a ring R with involution are investigated. An algebraic condition for the existence of an ordering of R is given. Also, a condition for enlarging an ordering of R to an overring is given. As for the case of a field, any preordering of R can be extended to some ordering. Finally, we investigate the class of archimedean ordered rings with involution.
Orderings of monomial ideals
We study the set of monomial ideals in a polynomial ring as an ordered set, with the ordering given by reverse inclusion. We give a short proof of the fact that every antichain of monomial ideals is finite. Then we investigate ordinal invariants for the complexity of this ordered set. In particular, we give an interpretation of the height function in terms of the Hilbert-Samuel polynomial, and we compute bounds on the maximal order type.
Orderings on semirings.
Orderings under field extensions.
Orders of non-commutative rings. (Ordnungen nichtkommutativer Ringe.)
Orders with ten elements are circle order.
Order-theoretic properties of some sets of quasi-measures
Let and be algebras of subsets of a set with , and denote by the set of all quasi-measure extensions of a given quasi-measure on to . We show that is order bounded if and only if it is contained in a principal ideal in if and only if it is weakly compact and is contained in a principal ideal in . We also establish some criteria for the coincidence of the ideals, in , generated by and .
Ordinal Bounds for Well Ordered Extensions of the Coordinatewise Partial Ordering
Ordres à distance minimum d'un tournoi et graphes partiels sans circuits maximaux
Ordres "C.A.C."
Ordres maximaux
Ordres partiels et permutoèdre
Orthocomplemented difference lattices with few generators
The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e. g., [19, 20]). Recently an effort has been exercised to advance with logics that possess a symmetric difference ([13, 14]) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In [13] the author constructs an ODL that is not set-representable. This example is quite elaborate. A main result...
Orthodox semigroups with complemented congruence lattices.
Orthogonal and prereflective subcategories
Orthogonal decompositions of MV-spaces.
A maximal disjoint subset S of an MV-algebra A is a basis iff {x in A : x ≤ a} is a linearly ordered subset of A for all a in S. Let Spec A be the set of the prime ideals of A with the usual spectral topology. A decomposition Spec A = Ui in I Ti U X is said to be orthogonal iff each Ti is compact open and S = {ai}i in I is a maximal disjoint subset. We prove that this decomposition is unrefinable (i.e. no Ti = Theta ∩ Y with Theta open, Theta ∩ Y = emptyset, int Y = emptyset) iff S is a basis. Many...