منابع مشابه
On 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 کاملSemigroups of inverse quotients
We examine, in a general setting, a notion of inverse semigroup of left quotients, which we call left I-quotients. This concept has appeared, and has been used, as far back as Clifford’s seminal work describing bisimple inverse monoids in terms of their right unit subsemigroups. As a consequence of our approach, we find a straightforward way of extending Clifford’s work to bisimple inverse semi...
متن کاملExpansions of Inverse Semigroups
We construct the freest idempotent-pure expansion of an inverse semigroup, generalizing an expansion of Margolis and Meakin for the group case. We also generalize the Birget-Rhodes prefix expansion to inverse semigroups with an application to partial actions of inverse semigroups. In the process of generalizing the latter expansion, we are led to a new class of idempotent-pure homomorphisms whi...
متن کاملBinary Relations as Lattice Isomorphisms
In 1963, Zaretskiùõ established a one-to-one correspondence between the set BX of binary relations on a set X and the set of triples of the form (W,φ, V ) where W and V are certain lattices and φ : W −→ V is an isomorphism. We provide a multiplication for these triples making the Zaretskiùõ correspondence a semigroup isomorphism. In addition, we consider faithful representations of BX by pairs ...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1978
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500016114