Left adequate and left Ehresmann monoids II
نویسندگان
چکیده
منابع مشابه
Left Adequate and Left Ehresmann Monoids Ii
This article is the second of two presenting a new approach to left adequate monoids. In the first, we introduced the notion of being T -proper, where T is a submonoid of a left adequate monoid M . We showed that the free left adequate monoid on a set X is X∗-proper. Further, any left adequate monoid M has an X∗-proper cover for some set X , that is, there is an X∗proper left adequate monoid M̂ ...
متن کاملStructure of Left Adequate and Left Ehresmann Monoids
This is the first of two articles studying the structure of left adequate and, more generally, of left Ehresmann monoids. Motivated by a careful analysis of normal forms, we introduce here a concept of proper for a left adequate monoid M . In fact, our notion is that of T -proper, where T is a submonoid of M . We show that any left adequate monoid M has an X∗proper cover for some set X , that i...
متن کاملEhresmann monoids
Ehresmann monoids form a variety of biunary monoids, that is, monoids equipped with two basic unary operations, the images of which coincide and form a semilattice of projections. The monoid of binary relations BX on any setX with unary operations of domain and range is Ehresmann. Inverse monoids, regarded as biunary submonoids of BX via the Wagner-Preston representation theorem, are therefore ...
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Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element $qin Q$ can be written as $q=a^{-1}b$ for some $a,bin S$. If we insist on $a$ and $b$ being $er$-related in $Q$, then we say that $S$ is straight in $Q$. We characterize semigroups which are left I-quotients of left regular bands of right cancell...
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We describe a class of monoids where c-rational languages can be deened analogously to trace theory and where these languages are precisely the recognizable ones. The proofs rely on Ramsey's theorem, distributive lattice theory and on Hashigushi's rank function generalized to our left divisibility monoids. We obtain Ochma nski's theorem on recognizable languages in free partially commutative mo...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2011
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2011.09.006