It is shown that the proof by Mehta and Parameswaran of Wahl’s conjecture for Grassmannians in positive odd characteristics also works for symplectic and orthogonal Grassmannians.
In an earlier paper, the authors showed that standard semigroups , and play an important role in the classification of weaker versions of alg-universality of semigroup varieties. This paper shows that quasivarieties generated by and are neither relatively alg-universal nor -universal, while there do exist finite semigroups and generating the same semigroup variety as and respectively and the quasivarieties generated by and/or are quasivar-relatively -alg-universal and -universal...
2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14H40, 20M14.Let H be a 4-semigroup, i.e., a numerical semigroup whose minimum positive element is four. We denote by 4r(H) + 2 the minimum element of H which is congruent to 2 modulo 4. If the genus g of H is larger than 3r(H) − 1, then there is a cyclic covering π : C −→ P^1 of curves with degree 4 and its ramification point P such that the Weierstrass semigroup H(P) of P is H (Komeda [1]). In this paper it is showed that...
Let S = {a,b,c,...} and Γ = {α,β,γ,...} be two nonempty sets. S is called a Γ -semigroup if aαb ∈ S, for all α ∈ Γ and a,b ∈ S and (aαb)βc = aα(bβc), for all a,b,c ∈ S and for all α,β ∈ Γ. In this paper we study the semidirect product of a semigroup and a Γ-semigroup. We also introduce the notion of wreath product of a semigroup and a Γ-semigroup and investigate some interesting properties of this product.