The amalgamation property of varieties determined by primitive lattices
The associative operad and the weak order on the symmetric groups.
The associativity equation revisited.
The Auslander-Reiten quiver for posets of finite growth
The axiomatic rank of the quasivariety of orderable groups is infinite.
The axioms for implication in orthologic
We set up axioms characterizing logical connective implication in a logic derived by an ortholattice. It is a natural generalization of an orthoimplication algebra given by J. C. Abbott for a logic derived by an orthomodular lattice.
The base-normed space of a unital group
The Bordalo order on a commutative ring
If is a commutative ring with identity and is defined by letting mean or , then is a partially ordered ring. Necessary and sufficient conditions on are given for to be a lattice, and conditions are given for it to be modular or distributive. The results are applied to the rings of integers mod for . In particular, if is reduced, then is a lattice iff is a weak Baer ring, and is a distributive lattice iff is a Boolean ring, , , or a four element field.
The Brooks-Jewett theorem for -triangular functions on difference posets and orthoalgebras
The Bruhat rank of a binary symmetric staircase pattern
In this work we show that the Bruhat rank of a symmetric (0,1)-matrix of order n with a staircase pattern, total support, and containing In, is at most 2. Several other related questions are also discussed. Some illustrative examples are presented.
The Cantor Extension of a Lexicographic Product of -Groups
The Cartesian product of sets and the Hessenberg natural product of ordinals
The categories of presheaves containing any category of algebras [Book]
The category of compactifications and its coreflections
We define “the category of compactifications”, which is denoted CM, and consider its family of coreflections, denoted corCM. We show that corCM is a complete lattice with bottom the identity and top an interpretation of the Čech–Stone . A corCM implies the assignment to each locally compact, noncompact a compactification minimum for membership in the “object-range” of . We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate the atoms...
The Cauchy extension of an ordered abelian group realized by -valuations
The cd-index of Bruhat intervals.
The chain of right simple semigroups in ordered semigroups
The characterization of -compact elements in some lattices
The Charney-Davis quantity for certain graded posets.
The Chinese remainder theorem and sheaf representations