A new type of semigroups which appears while dealing with N = 1 superconformal symmetry in superstring theories is considered. The ideal series having unusual abstract properties is constructed. Various idealisers are introduced and studied. The ideal quasicharacter is defined. Green’s relations are found and their connection with the ideal quasicharacter is established.

If N is a submodule of the R-module M , and a ∈ R, let λa : M/N → M/N be multiplication by a. We say that N is a primary submodule of M if N is proper and for every a, λa is either injective or nilpotent. Injectivity means that for all x ∈ M , we have ax ∈ N ⇒ x ∈ N . Nilpotence means that for some positive integer n, aM ⊆ N , that is, a belongs to the annihilator of M/N , denoted by ann(M/N). ...

Evolutionary processes are routinely modelled using 'ideal' Wright-Fisher populations of constant size N in which each individual has an equal expectation of reproductive success. In a hypothetical ideal population, variance in reproductive success (V(k)) is binomial and effective population size (N(e)) = N. However, in any actual implementation of the Wright-Fisher model (e.g., in a computer),...

We determine a Gröbner basis for the secant ideal of the toric ideal associated to the second hypersimplex ∆(2, n), with respect to any circular term order. The Gröbner basis of the secant ideal requires polynomials of odd degree up to n. This shows that the circular term order is 2-delightful, resolving a conjecture of Drton, Sturmfels, and the author. The proof uses Gröbner degenerations for ...

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In [25], Kostyrko et. al introduced the concept of ideal convergence as a sequence (xk) of real numbers is said to be I-convergent to a real number `, if for each ε > 0 the set {k ∈ N : |xk − `| ≥ ε} belongs to I. In this article we introduce the concept of ideal conv...

√(f1,...,fd+1)R[X] [3,p.124]. The question is whether an ideal (f1,...,fd+1) R[X] can be chosen as a reduction of I. We only know the following case of affine domains, which was developed by G. Lyubeznik [4]: Let R be an n-dimensional affine domain over an infinite field k and let I be an ideal of R. Then I has a reduction generated by n+1 elements. He also posed the following conjecture: Let A...

Cryptographic multilinear maps have many applications, such as multipartite key exchange and software obfuscation. However, the encodings of three current constructions are “noisy” and their multilinearity levels are fixed and bounded in advance. In this paper, we describe a candidate construction of ideal multilinear maps by using ideal lattices, which supports arbitrary multilinearity levels....

Cryptographic multilinear maps have many applications, such as multipartite key exchange and software obfuscation. However, the encodings of three current constructions are “noisy” and their multilinearity levels are fixed and bounded in advance. In this paper, we describe a candidate construction of ideal multilinear maps by using ideal lattices, which supports arbitrary multilinearity levels....

Let $L$ be a completely regular frame and $mathcal{R}L$ be the ‎ring of continuous real-valued functions on $L$‎. ‎We show that the‎ ‎lattice $Zid(mathcal{R}L)$ of $z$-ideals of $mathcal{R}L$ is a‎ ‎normal coherent Yosida frame‎, ‎which extends the corresponding $C(X)$‎ ‎result of Mart'{i}nez and Zenk‎. ‎This we do by exhibiting‎ ‎$Zid(mathcal{R}L)$ as a quotient of $Rad(mathcal{R}L)$‎, ‎the‎ ‎...

Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x 1 ,. .. , x n ] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi's theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and im...