相关论文: 2 x 2 permanental ideals of hypermatrices
In this article, we study the ideal generated by $2\times 2$ permanents of a symmetric matrix. We denote this ideal by $P_2(X)$ where $X$ is a symmetric matrix. We compute a Gr\"obner basis, dimension, depth, minimal primes, and a primary…
The principal result is a primary decomposition of ideals generated by the (2x2)-subpermanents of a generic matrix. These permanental ideals almost always have embedded components and their minimal primes are of three distinct heights. Thus…
We introduce the concept of s-Hankel hypermatrix, which generalizes both Hankel matrices and generic hypermatrices. We study two determinantal ideals associated to an s-Hankel hypermatrix: the ideal I<s,t> generated by certain 2 x 2 slice…
We describe the minimal free resolution of the ideal of $2 \times 2$ subpermanents of a $2 \times n$ generic matrix $M$. In contrast to the case of $2 \times 2$ determinants, the $2 \times 2$ permanents define an ideal which is neither…
In this paper we discuss minimal primes over permanental ideals of generic matrices. We give a complete list of the minimal primes over ideals of 3 x 3 permanents of a generic matrix, and show that there are monomials in the ideal of…
We provide the Grobner basis and the primary decomposition of the ideals generated by 2 by 2 permanents of Hankel matrices.
Multiplicative hyperrings are an important class of algebraic hyperstructures which generalize rings further to allow multiple output values for the multiplication operation. Let R be a commutative multiplicative hyperring. The 2-prime…
We describe the equivariant syzygies of the ideal of $2 \times 2$ permanents of a generic $2 \times n$ matrix under its natural symmetric and torus group actions. Our proof gives us a new method of finding the Betti numbers of this ideal,…
We consider ideals arising in the context of conditional independence models that generalize the class of ideals considered by Fink [7] in a way distinct from the generalizations of Herzog-Hibi-Hreinsdottir-Kahle-Rauh [13] and Ay-Rauh [1].…
In this paper, we introduce the concepts of strongly 2-absorbing primary ideals (resp., submodules) and strongly 2-absorbing ideals (resp., submodules) as generalizations of strongly prime ideals. Furthermore, we investigate some basic…
In this paper we study primality and primary decomposition of certain ideals which are generated by homogeneous degree $2$ polynomials and occur naturally from determinantal conditions. Normality is derived from these results.
Let $X$ be a matrix of indeterminates, $t$ an integer, and $P_t(X)$ define the ideal generated by the permanents of all $t\times t$ submatrix of $X$. $P_t(X)$ is called a permanental ideal. In this article, we study the algebras…
In this study, we introduce the concept of "uniformly 2-absorbing primary ideals" of commutative rings, which imposes a certain boundedness condition on the usual notion of 2-absorbing primary ideals of commutative rings. Then we…
In this paper we study ideals generated by quite general sets of 2-minors of an $m \times n$-matrix of indeterminates. The sets of 2-minors are defined by collections of cells and include 2-sided ladders. For convex collections of cells it…
Let I be either the ideal of maximal minors or the ideal of 2-minors of a row graded or column graded matrix of linear forms L. In two previous papers we showed that I is a Cartwright-Sturmfels ideal, that is, the multigraded generic…
We give a description of the minimal primes of the ideal generated by the 2 x 2 adjacent minors of a generic matrix. We also compute the complete prime decomposition of the ideal of adjacent m x m minors of an m x n generic matrix when the…
We show that the apolar ideal to the determinant of a generic symmetric matrix is generated in degree two, and the apolar ideal to the permanent of a generic symmetric matrix is generated in degrees two and three. In each case we specify…
We describe the universal Groebner basis of the ideal of maximal minors and the ideal of $2$-minors of a multigraded matrix of linear forms. Our results imply that the ideals are radical and provide bounds on the regularity. In particular,…
Primary hyperideals have been introduced and studied in multiplicative hyperrings. In this paper, we intend to study extensively primary hyperideals of multiplicative hyperrings with absorbing zero and prove some results regarding them.…
Following the approach in the book "Commutative Algebra", by D. Eisenbud, where the author describes the generic initial ideal by means of a suitable total order on the terms of an exterior power, we introduce first the generic initial…