相关论文: Minimal generating sets for the first syzygies of …
In this paper, we determine minimal generating sets for several well-known monoids of matrices over semirings. In particular, we find minimal generating sets for the monoids consisting of: all $n\times n$ boolean matrices when $n\leq 8$;…
It is known that for a monomial ideal $I$, the number of minimal generators, $\mu(I^n)$, eventually follows a polynomial pattern for increasing $n$. In general, little is known about the power at which this pattern emerges. Even less is…
We describe a generating set for the initial ideal of simplicial toric ideals with respect to the graded reverse lexicographic order, using representations of elements of affine monoids as sums of irreducible elements. Although the…
For a monomial ideal $I$, let $G(I)$ be its minimal set of monomial generators. If there is a total order on $G(I)$ such that the corresponding Lyubeznik resolution of $I$ is a minimal free resolution of $I$, then $I$ is called a Lyubeznik…
A subset $S$ of a group $G$ invariably generates $G$ if, when each element of $S$ is replaced by an arbitrary conjugate, the resulting set generates $G.$ An invariable generating set $X$ of $G$ is called minimal if no proper subset of $X$…
We show that the number of elements generating a squarefree monomial ideal up to radical can always be bounded above in terms of the number of its minimal monomial generators and the maximal height of its minimal primes.
Let $I$ be a monomial ideal in two variables generated by three monomials and let $\mathcal{R}(I)$ be its Rees ideal. We describe an algorithm to compute the minimal generating set of $\mathcal{R}(I)$. Based on the data obtained by this…
A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,...,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of…
We display a new family of prime ideals with unbounded minimal number of generators in a three-dimensional power series ring over a field of characteristic zero. These primes are obtained as the kernel of a quasi-monomial algebra…
We find some sufficient conditions under which the permutational wreath product of two groups has a minimal generating set. In particular we prove that for a regular rooted tree the group of all automorphisms and the group of all…
In this paper, we deal with the problem of uniqueness of minimal system of binomial generators of a semigroup ideal. Concretely, we give different necessary and/or sufficient conditions for uniqueness of such minimal system of generators.…
We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the…
Using the Rowland idea, we find two infinite sets of generators of primes. We also pose some conjectures concerning twin primes.
Does there exist for any $\sigma$-algebra a minimal (with respect to inclusion) generating set? We formulate this problem and answer it in the very special instance of partition generated and standard measurable spaces, the general case…
We determine whether each known generating set of arbitrary oriented Reidemeister moves is minimal. We then provide a complete classification of minimal generating sets that include a coherent Reidemeister move of type II. We also classify…
Given an algebra $F[H]^G$ of polynomial invariants of an action of the group $G$ over the vector space $H$, a subset $S$ of $F[H]^G$ is called separating if $S$ separates all orbits that can be separated by $F[H]^G$. A minimal separating…
Given an initial family of sets, we may take unions, intersections and complements of the sets contained in this family in order to form a new collection of sets; our construction process is done recursively until we obtain the last family.…
We present a class of homogeneous ideals which are generated by monomials and binomials of degree two and are set-theoretic complete intersections. This class includes certain reducible varieties of minimal degree and, in particular, the…
We obtain several presentations by generators and relations for the rook partition monoids and algebras, as well as their singular ideals. Among other results, we also calculate the minimal sizes of generating sets (some of our…
It is shown that any set of nonzero monomial prime ideals can be realized as the stable set of associated prime ideals of a monomial ideal. Moreover, an algorithm is given to compute the stable set of associated prime ideals of a monomial…