共查询到20条相似文献,搜索用时 500 毫秒
1.
Peter R. Jones 《Semigroup Forum》2006,73(3):330-344
A lattice isomorphism between inverse semigroups S and T is an isomorphism between their lattices of inverse subsemigroups.
When S is combinatorial, 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 isomorphism. Since lattice-isomorphic groups need not have the same cardinality, extending these techniques
to the non-combinatorial case requires some means of tying the subgroups to the rest of the semigroup. Ershova showed that
if S has no nontrivial isolated subgroups (subgroups that form an entire D-class) then again a bijection exists between S
and T. Recently, this technique has been successfully exploited, by Goberstein for fundamental inverse semigroups and by
the author for completely semisimple inverse semigroups, under two different finiteness hypotheses. In this paper, we derive
further properties of Ershova's bijection(s) and formulate a "quasi-connected" hypothesis that enables us to derive both Goberstein's
and the author's earlier results as corollaries. 相似文献
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In this paper, we consider the lattice Subf S of full subsemigroups of an inverse semigroup S. Our first main theorem states
that for any inverse semigroup S, Subf S is a subdirect product of the lattices of full subsemigroups of its principal factors,
so that Subf S is distributive [meet semidistributive, join semidistributive, modular, semimodular] if and only if the lattice
of full subsemigroups of each principal factor is. To examine such inverse semigroups, therefore, we need essentially only
consider those which are 0-simple. For a 0-simple inverse semigroup S (not a group with zero), we show that in fact each of
modularity, meet semidistributivity and join semidistributivity of Subf S is equivalent to distributivity of S, that is, S
is the combinatorial Brandt semigroup
with exactly two nonzero idempotents and two nonidempotents. About semimodularity, however, we concentrate only on the completely
0-simple case, that is, Brandt semigroups. For a Brandt semigroup S (not a group with zero), semimodularity of Subf S is equivalent
to distributivity of Subf S. Finally, we characterize an inverse semigroup S for which Subf S is a chain. 相似文献
4.
We investigate certain semigroup varieties formed by nilpotent extensions of
orthodox normal bands of commutative periodic groups. Such semigroups are shown
to be both structurally periodic and structurally commutative, and are therefore
structurally inverse semigroups. Such semigroups are also shown to be dense
semilattices of structurally group semigroups. Making use of these structure
decompositions, we prove that the subvariety lattice of any variety comprised of
such semigroups is isomorphic to the direct product of the following three
sublattices: its sublattice of all structurally trivial semigroup varieties, its
sublattice of all semilattice varieties, and its sublattice of all group
varieties. We conclude, therefore, that to completely describe this lattice, we
must first describe completely the lattice of all structurally trivial semigroup
varieties, since the other two are well known lattices. 相似文献
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Alexei Vernitski 《Semigroup Forum》2009,78(3):486-497
We prove a number of results related to finite semigroups and their inverse subsemigroups, including the following. (1) A finite
semigroup is aperiodic if and only if it is a homomorphic image of a finite semigroup whose inverse subsemigroups are semilattices.
(2) A finite inverse semigroup can be represented by order-preserving mappings on a chain if and only if it is a semilattice.
Finally, we introduce the concept of pseudo-small quasivariety of finite semigroups, generalizing the concept of small variety. 相似文献
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In a paper published in 1994, Umar defined an interesting class of transformation semigroups which naturally generalizes the Vagner one-point completion of the symmetric inverse semigroup. In this paper we prove some isomorphism theorems for finite such semigroups and compute their ranks. Moreover, we determine all maximal inverse subsemigroups of an arbitrary transformation semigroup of this type which is not inverse. 相似文献
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This paper recalls some properties of a cyclic semigroup and examines cyclic subsemigroups in a finite ordered semigroup. We prove that a partially ordered cyclic semigroup has a spiral structure which leads to a separation of three classes of such semigroups. The cardinality of the order relation is also estimated. Some results concern semigroups with a lattice order. 相似文献
13.
Peter R. Jones 《Semigroup Forum》2013,86(2):337-361
The left restriction semigroups have arisen in a number of contexts, one being as the abstract characterization of semigroups of partial maps, another as the ‘weakly left E-ample’ semigroups of the ‘York school’, and, more recently as a variety of unary semigroups defined by a set of simple identities. We initiate a study of the lattice of varieties of such semigroups and, in parallel, of their two-sided versions, the restriction semigroups. Although at the very bottom of the respective lattices the behaviour is akin to that of varieties of inverse semigroups, more interesting features are soon found in the minimal varieties that do not consist of semilattices of monoids, associated with certain ‘forbidden’ semigroups. There are two such in the one-sided case, three in the two-sided case. Also of interest in the one-sided case are the varieties consisting of unions of monoids, far indeed from any analogue for inverse semigroups. In a sequel, the author will show, in the two-sided case, that some rather surprising behavior is observed at the next ‘level’ of the lattice of varieties. 相似文献
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Akihiro Yamamura 《Journal of Pure and Applied Algebra》2007,210(2):521-536
A variant of an HNN extension of an inverse semigroup introduced by Gilbert [N.D. Gilbert, HNN extensions of inverse semigroups and groupoids, J. Algebra 272 (2004) 27-45] is defined provided that associated subsemigroups are order ideals. We show this presentation still makes sense without the assumption on associated subsemigroups in the sense that it gives a semigroup deserving to be an HNN extension, and it is embedded into another variant using the automata theoretical technique based on combinatorial and geometrical properties of Schützenberger graphs. 相似文献
16.
李师正 《纯粹数学与应用数学》1993,9(1):105-111
每个子半群是左理想的半群,称为左Hamilton半群,本文给出左Hamilton半群的刻划,并将左Hamilton半群表示为有向森林,最后给出左Hamilton半群同构的充要条件。 相似文献
17.
本文考虑全正则子半群构成链的正则半群,得到了正则半群具有全正则子半群构成链的一个充分必要条件,这推广了Jones关于具有全正则子半群构成链的逆半群的结果.特别地,建立了具有全正则子半群构成链的完全0-单半群的结构. 相似文献
18.
A filter in a semigroup is a subsemigroup whose complement is an ideal. (Alternatively, in a quasiordered semigroup, a slightly more general definition can be given.) We prove a number of results related to filters in a semigroup and the lattice of filters of a semigroup. For instance, we prove that every complete algebraic lattice can be the lattice of filters of a semigroup. We prove that every finite semigroup is a homomorphic image of a finite semigroup whose lattice of filters is boolean and which belongs to the pseudovariety generated by the original semigroup. We describe filter lattices of some well-known semigroups such as full transformation semigroups of finite sets (which are three-element chains) and free semigroups (which are boolean). 相似文献
19.
Mario Petrich 《Semigroup Forum》2003,66(3):381-400
We characterize orthogroups, local orthogroups and (left,right) cryptogroups within completely regular semigroups by means of absence of certain kind of subsemigroups. For each of these varieties V, we determine the complete set of minimal non-V -varieties. For each of the latter varieties, we determine the lattice of its subvarieties. We then give a generating semigroup and a basis of its identities for every variety which occurs in this way. The subvariety lattices are illustrated by three diagrams. 相似文献
20.
Abstract. A topologized semigroup is called perfect if its multiplication is a perfect map (= a closed continuous mapping such that the inverse image of every point is compact).
Thus a locally compact topological semigroup is perfect if and only if its multiplication is closed and each of its elements
is compactly divided , that is, its divisors form a compact set. In the present paper we study compactly and non-compactly divided elements in
the contexts of general locally compact semigroups, subsemigroups of groups, Lie semigroups and subsemigroups of Sl(2,R). 相似文献