On a Class of Lattice Ordered Inverse Semigroups
نویسندگان
چکیده
منابع مشابه
Semilattice ordered inverse semigroups
As Jonathan Leech has pointed out, many natural examples of inverse semigroups are semilattice ordered under the natural partial order. But there are many interesting examples of semilattice ordered inverse semigroups in which the imposed partial order is not the natural one. In this talk we shall explore the structure and properties of these examples and some other questions related to semilat...
متن کاملOn lattice isomorphisms of inverse semigroups, II
A lattice isomorphism between inverse semigroups S and T is an isomorphism between their lattices of inverse subsemigroups. When S is aperiodic, it has long been known that a bijection is induced between S and T . Various authors have introduced successively weaker ‘archimedean’ hypotheses under which this bijection is necessarily an isomorphism, naturally inducing the original lattice isomorph...
متن کاملOn lattice isomorphisms of inverse semigroups
An L-isomorphism between inverse semigroups S and T is an isomorphism between their lattices L(S) and L(T ) of inverse subsemigroups. The author and others have shown that if S is aperiodic – has no nontrivial subgroups – then any such isomorphism Φ induces a bijection φ between S and T . We first characterize the bijections that arise in this way and go on to prove that under relatively weak ‘...
متن کاملOn a Class of Lattice-ordered Rings
for some real number X, the symbol V denoting the lattice least upper bound. Any ring R is regular [10] if for each xER there is an xaER such that xx°x = x. It is evident that every regular F-ring R contains a maximal bounded sub-F-ring R, the F-ring of all xER satisfying equation (1.1). The relationship between a regular F-ring and its maximal bounded sub-F-ring is analogous to that between th...
متن کاملA Class of Simple Lattice-ordered Groups
A lattice-ordered group (/-group) is said to be regular il no positive element of the group is disjoint from any of its conjugates. It is well known that every simple regular /-group is totally ordered [S]. The subgroups of the reals are the most elementary examples of regular simple /-groups; other examples can be found in [2] and [ó]. In this note we investigate a class of simple /-groups at ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2000
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8324