The first collection of a macrofungal agaric species, with morphological features similar to already described Anamika species, has been found in association with animal bones in north Queensland, Australia. This species also shares features with several, commonly occurring and previously described Australian Hebeloma species. An integrated morphological and molecular study has resulted in the ...

Given two numerical semigroups S and T and a positive integer d, S is said to be one over d of T if S = {s ∈ N | ds ∈ T} and in this case T is called a d-fold of S. We prove that the minimal genus of the d-folds of S is g + ⌈ (d−1)f 2 ⌉, where g and f denote the genus and the Frobenius number of S. The case d = 2 is a problem proposed by Robles-Pérez, Rosales, and Vasco. Furthermore, we find th...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

Let A be an n-dimensional algebra over a field k and a(A) its quantum symmetry semigroup. We prove that the automorphisms group \(\mathrm{Aut}_{\mathrm{Alg}} (A)\) of is isomorphic to \(U \bigl ( G(a (A)^{\mathrm{o}} ) )\) all invertible group-like elements finite dual \(a (A)^{\mathrm{o}}\). For G, G-gradings on are explicitly described classified: set isomorphisms classes in bijection with qu...

An absolutely continuous free semigroup algebra is weak-∗ type L. A free semigroup algebra is the wot-closed (nonself-adjoint, unital) algebra S generated by n isometries S1, . . . , Sn with pairwise orthogonal ranges. See [4] for an introduction. There is now a significant literature on these algebras [1, 2, 9, 10, 11, 7, 6, 8, 5, 16, 15, 18, 17, 20]. The prototype is the non-commutative Toepl...

There is a substantial theory (modelled on permutation representations of groups) of representations of an inverse semigroup S in a symmetric inverse monoidIX , that is, a monoid of partial one-to-one selfmaps of a set X . The present paper describes the structure of a categorical dual I Ł X to the symmetric inverse monoid and discusses representations of an inverse semigroup in this dual symme...

Let X∗ be a free monoid over an alphabet X and W be a finite language over X. Let S(W ) be the Rees quotient X∗/I(W ), where I(W ) is the ideal of X∗ consisting of all elements of X∗ that are not subwords of W . Then S(W ) is a finite monoid with zero and is called the discrete syntactic monoid of W . W is called finitely based if the monoid S(W ) is finitely based. In this paper, we give some ...

Let D be the ring of differential operators on a smooth irreducible affine variety X over C; or, more generally, the enveloping algebra of any locally free Lie algebroid on X. The category of finitely-generated graded modules of the Rees algebra e D has a natural quotient category qgr( e D) which imitates the category of modules on Proj of a graded commutative ring. We show that the derived cat...

Let I be a monomial ideal in a polynomial ring over a field k. If the Rees cone of I is quasi-ideal, we express the normalization of the Rees algebra of I in terms of an Ehrhart ring. We introduce the basis Rees cone of a matroid and study their facets. Then an application to Rees algebras is presented.