Lattice isomorphisms of orthodox semigroups
نویسندگان
چکیده
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 کاملBeyond Orthodox Semigroups
We introduce the notions of a generalised category and of an inductive generalised category over a band. Our purpose is to describe a class of semigroups which we name weakly B-orthodox. In doing so we produce a new approach to characterising orthodox semigroups, by using inductive generalised groupoids. Here B denotes a band of idempotents; we note that if B is a semilattice then a weakly B-or...
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 ...
متن کاملIsomorphisms and strong finite projec- tive classes of commutative semigroups
In “Sverdlovsk notebook” (Sverdlovsk, 1969), I proposed a question: Are any too first-order equivalent finitely generated commutative semigroups isomorphic? In 1970, B.I.Zilber answered the question negatively. A question arises: In what language, any equivalent over the language finitely generated commutative semigroups are isomorphic? In the note, we propose such a language. Moreover, we prov...
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: Bulletin of the Australian Mathematical Society
سال: 1992
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700030069