Semigroup Forum最新文献

Let T(X) (resp. L(V)) be the semigroup of all transformations (resp. linear transformations) of a set X (resp. vector space V). For a subset Y of X and a subsemigroup (mathbb {S}(Y)) of T(Y), consider the subsemigroup (T_{mathbb {S}(Y)}(X) = {fin T(X):f_{upharpoonright _Y} in mathbb {S}(Y)}) of T(X), where (f_{upharpoonright _Y}in T(Y)) agrees with f on Y. We give a new characterization for (T_{mathbb {S}(Y)}(X)) to be a regular semigroup [inverse semigroup]. For a subspace W of V and a subsemigroup (mathbb {S}(W)) of L(W), we define an analogous subsemigroup (L_{mathbb {S}(W)}(V) = {fin L(V) :f_{upharpoonright _W} in mathbb {S}(W)}) of L(V). We describe regular elements in (L_{mathbb {S}(W)}(V)) and determine when (L_{mathbb {S}(W)}(V)) is a regular semigroup [inverse semigroup, completely regular semigroup]. If (mathbb {S}(Y)) (resp. (mathbb {S}(W))) contains the identity of T(Y) (resp. L(W)), we describe unit-regular elements in (T_{mathbb {S}(Y)}(X)) (resp. (L_{mathbb {S}(W)}(V))) and determine when (T_{mathbb {S}(Y)}(X)) (resp. (L_{mathbb {S}(W)}(V))) is a unit-regular semigroup.

Cameron et al. determined the maximum size of a null subsemigroup of the full transformation semigroup (mathcal {T}(X)) on a finite set X and provided a description of the null semigroups that achieve that size. In this paper we extend the results on null semigroups (which are commutative) to commutative nilpotent semigroups. Using a mixture of algebraic and combinatorial techniques, we show that, when X is finite, the maximum order of a commutative nilpotent subsemigroup of (mathcal {T}(X)) is equal to the maximum order of a null subsemigroup of (mathcal {T}(X)) and we prove that the largest commutative nilpotent subsemigroups of (mathcal {T}(X)) are the null semigroups previously characterized by Cameron et al.

Let E be an equivalence on a set X and let (T_exists (X)) denote the semigroup (under composition) of all (f:Xrightarrow X) that reflect E. Fix an element (theta in T_exists (X)) and for (f,gin T_exists (X)), define a new operation (*) on (T_exists (X)) by (f* g=ftheta g) where (ftheta g) denotes the product of (g,theta ) and f in the original sense. In this paper, we characterize Green’s relations on the variant semigroups (T_exists (X,theta )) of (T_exists (X)) with sandwich operation (theta ).

Grillet (Semigroup Forum 50:25–36, 1995) introduced the concept of stratified semigroups as a kind of generalisation of finite nilsemigroups. We extend Grillet’s ideas by introducing the notion of the base of a semigroup and show that a semigroup is stratified if and only if its base is either empty or consists of only the zero element. The general structure of semigroups with non-trivial bases is studied and we show that these can be described in terms of ideal extensions of semigroups by stratified semigroups. We consider certain types of group-bound semigroups and also ideal extensions of Clifford semigroups, and show how to describe them as semilattices of ideal extensions by stratified semigroups and provide a number of interesting examples.

This paper is concerning with the study of stability involving a thermoelastic system with internal nonlinear localized damping. The main novelty of the paper is to introduce to the study of thermoelastic system the general Wentzell boundary conditions associated to the internal heat equation. This boundary condition takes into account that there is a boundary source of heat which depends on the heat flow along the boundary, the heat flux across the boundary, and the temperature at the boundary. The tools are the use of multipliers with the construction of appropriate perturbed energy functionals.

We introduce the notion of PC cancellative additive monoids with infinity and use it to characterize cancellative additive principal ideal domains with infinity. Our characterization improves various known characterizations from the literature, both, in the context of the commutative cancellative monoids, as well as in the context of the analogues of the statements from the commutative ring theory.

The plactic monoids can be obtained from the tensor product of crystals. Similarly, the hypoplactic monoids can be obtained from the quasi-tensor product of quasi-crystals. In this paper, we present a unified approach to these constructions by expressing them in the context of quasi-crystals. We provide a sufficient condition to obtain a quasi-crystal monoid for the quasi-tensor product from a quasi-crystal monoid for the tensor product. We also establish a sufficient condition for a hypoplactic monoid to be a quotient of the plactic monoid associated to the same seminormal quasi-crystal.

Relying on the notions of submodular function and partial metric, we introduce normed inverse semigroups as a generalization of normed groups and sup-semilattices equipped with an upper valuation. We define the property of skew-convexity for a metric on an inverse semigroup, and prove that every norm on a Clifford semigroup gives rise to a right-subinvariant and skew-convex metric; it makes the semigroup into a Hausdorff topological inverse semigroup if the norm is cyclically permutable. Conversely, we show that every Clifford monoid equipped with a right-subinvariant and skew-convex metric admits a norm for which the metric topology and the norm topology coincide. We characterize convergence of nets and show that Cauchy completeness implies conditional monotone completeness with respect to the natural partial order of the inverse semigroup.

In this paper we give growth estimates for (Vert T^nVert ) for (nrightarrow infty ) in the case T is a strongly Kreiss bounded operator on a ({{,textrm{UMD},}}) Banach space X. In several special cases we provide explicit growth rates. This includes known cases such as Hilbert and (L^p)-spaces, but also intermediate ({{,textrm{UMD},}}) spaces such as non-commutative (L^p)-spaces and variable Lebesgue spaces.

We study a submonoid of the well studied monoid (POI_n) of all order-preserving partial injections on an n-element chain. The set (IOF_n^{par}) of all partial transformations in (POI_n) which are fence-preserving as well as parity-preserving forms a submonoid of (POI_n). We describe Green’s relations and ideals of (IOF_n^{par}). For each ideal of (IOF_n^{par}), we characterize the maximal subsemigroups. We observe that there are three different types of maximal subsemigroups.