We study the Cox realization of an affine variety, i.e., a canonical representation of a normal affine variety with finitely generated divisor class group as a quotient of a factorially graded affine variety by an action of the Neron-Severi quasitorus. The realization is described explicitly for the quotient space of a linear action of a finite group. A universal property of this realization is...

A language L over an alphabet Σ is prefix-convex if, for any words x, y, z ∈ Σ, whenever x and xyz are in L, then so is xy. Prefix-convex languages include right-ideal, prefixclosed, and prefix-free languages. We study complexity properties of prefix-convex regular languages. In particular, we find the quotient/state complexity of boolean operations, product (concatenation), star, and reversal,...

A variety of semigroups that is minimal with respect to being non-finitely based is said to be a limit variety. By Zorn’s Lemma, each non-finitely based variety contains at least one limit subvariety. Although many examples of non-finitely based varieties are known in the literature (see [3, 5]), explicit examples of limit varieties are very rarely discovered [1, 2, 4]. The objective of the pre...

In [2], Bost and Connes studied a particular Hecke C-algebra CQ arising in number theory. The algebra CQ can be realised as a semigroup crossed product C (Q/Z)⋊αN ∗ by an endomorphic action α of the multiplicative semigroup N on the group Calgebra C(Q/Z) [7], and this realisation has provided useful insight into the analysis of CQ [5, 13]. Since individual elements of Q/Z and N ∗ involve only f...

A weight ring in type A is the coordinate ring of the GIT quotient of the variety of flags in Cn modulo a twisted action of the maximal torus in SL(n, C). We show that any weight ring in type A is generated by elements of degree strictly less than the Krull dimension, which is at worst O(n). On the other hand, we show that the associated semigroup of Gelfand–Tsetlin patterns can have an essenti...

Algebraic properties and structures of intuitionistic $$L-$$ fuzzy multiset finite automata (ILFMA) are discussed through congruences on a semigroup in this paper. Firstly, we put forward the notion compatible relation, monoid associated with relation can be effectively constructed, construct two monoids different congruence relations given ILFMA, then prove that they isomorphic. Furthermore, u...

S OF PAPERS SUBMITTED FOR PRESENTATION TO THE SOCIETY The following papers have been submitted to the Secretary and the Associate Secretaries of the Society for presentation at meetings of the Society. They are numbered serially throughout this volume. Cross references to them in the reports of the meetings will give the number of this volume, the number of this issue, and the serial number of ...

A poset is said to be ω-chain complete if every countable chain in it has a least upper bound. It is known that every partially ordered set has a natural ω-completion. In this paper we study the ω-completion of partially ordered semigroups, and the topological action of such a semigroup on its ω-completion. We show that, for partially ordered semigroups, ω-completion and quotient with respect t...

Objectives/Background: The ternary seminear ring is the generalization of and it need not be a semiring. Characterization quotient rings some structures have been analysed also studied ideals in rings. Further quasi defined discussed about their properties. Methods: Properties semiring employed to carry out this research work obtain all characterizations corresponding that Findings: We call an ...