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Ideals of Herzog–Northcott type

Abstract This paper takes a new look at ideals generated by 2×2 minors of 2×3 matrices whose entries are powers of three elements not necessarily forming a regular sequence. A special case of this is…
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Degree and Algebraic Properties of Lattice and Matrix Ideals

We study the degree of nonhomogeneous lattice ideals over arbitrary fields, and give formulas to compute the degree in terms of the torsion of certain factor groups of $\mathbb{Z}^s$ and in terms of…
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Rings of weak dimension one and syzygetic ideals

. We prove that rings of weak dimension one are the rings with all (three-generated) ideals syzygetic. This leads to a characterization of these rings in terms of the Andr(cid:19)e-Quillen homology.
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Degree and algebraic properties of lattice and binomial matrix ideals

On the module of effective relations of a standard algebra

Let A be a commutative ring. We denote by a standard A-algebra a commutative graded A-algebra U=[oplus ]n[ges ]0Un with U0=A and such that U is generated as an A-algebra by the elements of U1. Take x…
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The equations of Rees algebras of equimultiple ideals of deviation one

We describe the equations of the Rees algebra R(I) of an equimultiple ideal I of deviation one provided that I has a reduction generated by a regular sequence x1, . . . , xs such that the initial…
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Sally’s question and a conjecture of shimoda

Abstract In 2007, Shimoda, in connection with a long-standing question of Sally, asked whether a Noetherian local ring, such that all its prime ideals different from the maximal ideal are complete…
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Regular local rings of dimension four and Gorenstein syzygetic prime ideals

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Noetherian rings of low global dimension and syzygetic prime ideals

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The primary components of positive critical binomial ideals

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