We show that the (2 × 2)-subpermanents of a generic matrix generate an ideal whose height, unmixedness, primary decomposition, the number and structure of the minimal components, resolutions, radical, integral closure and Gröbner bases all depend on the characteristic of the underlying subfield: if the characteristic of the subfield is two, this ideal is the determinantal ideal for which all of...

It has been recently proved that a variety of associative PI-superalgebras with graded involution finite basic rank over field characteristic zero is minimal fixed ⁎-graded exponent if, and only it generated by subalgebra an upper block triangular matrix algebra, A:=UTZ2⁎(A1,…,Am), equipped suitable elementary Z2-grading involution. Here we give necessary sufficient conditions so IdZ2⁎(A) facto...

We introduce the notion of Gröbner S-basis of an ideal of the free associative algebra K〈X〉 over a field K invariant under the action of a semigroup S of endomorphisms of the algebra. We calculate the Gröbner S-bases of the ideal corresponding to the universal enveloping algebra of the free nilpotent of class 2 Lie algebra and of the T-ideal generated by the polynomial identity [x, y, z] = 0, w...

Let A be the ring obtained by localizing the polynomial ring κ[X, Y, Z, W ] over a field κ at the maximal ideal (X, Y, Z, W) and modulo the ideal (XW − Y Z). Let p be the ideal of A generated by X and Y. We study the module structure of a minimal injective resolution of A/p in details using local cohomology. Applications include the description of Ext i A (M, A/p), where M is a module construct...

Let A be the ring obtained by localizing the polynomial ring κ[X,Y, Z,W ] over a field κ at the maximal ideal (X, Y, Z,W ) and modulo the ideal (XW − Y Z). Let p be the ideal of A generated by X and Y . We study the module structure of a minimal injective resolution of A/p in details using local cohomology. Applications include the description of Ext A (M,A/p), where M is a module constructed b...

Theorem. A commutative B*-algebra K containing an identity e (with \\k*-k\\ =\\k\\2for all &GP and ||e|| =1) is isomorphic (in a norm and * preserving manner) to an algebra B(X) of all bounded complexvalued functions on an essentially unique set X if and only if: (1) Every nonzero closed ideal of K contains a minimal ideal; (2) The sum of two annulets is an annulet. An annulet is here understoo...

In this article, we study the jumping numbers of an ideal in the local ring at rational singularity on a complex algebraic surface. By understanding the contributions of reduced divisors on a fixed resolution, we are able to present an algorithm for finding of the jumping numbers of the ideal. This shows, in particular, how to compute the jumping numbers of a plane curve from the numerical data...

The Riemann-Roch theorem on a graph G is closely related to Alexander duality in combinatorial commutive algebra. We study the lattice ideal given by chip firing on G and the initial ideal whose standard monomials are the G-parking functions. When G is a saturated graph, these ideals are generic and the Scarf complex is a minimal free resolution. Otherwise, syzygies are obtained by degeneration...

An important predictor of historical sound change, functional load, fails to capture insights from speech perception. Building on ideal observer models of word recognition, we devise a new definition of functional load that incorporates both a priori expectedness and perceptual information. We explore this new measure with a simple model and find that it outperforms tra-

It is well-known that the Plücker relations generate the ideal of relations of the maximal minors of a generic m× n matrix. In this paper we discuss the relations of t-minors for t < min(m,n). We will exhibit minimal relations in degrees 2 (non-Plücker in general) and 3, and give some evidence for our conjecture that we have found the generating system of the ideal of relations. The approach is...