Ideal Observer Analysis Wilson S. Geisler University of Texas at Austin (to appear in Visual Neurosciences, MIT press) 1.0 Introduction................................................................................................................... 1 2.0 Basic concepts and formulas......................................................................................... 2 2.1 Bayesian ideal ob...

We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and it has numerous applications within and beyond pure mathematics. The ideals defining toric varieties are precisely the binomial prime ideals. Our main result...

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

We introduce a monomial ideal whose standard monomials encode the vertices of all fibers of a lattice. We study the minimal generators, the radical, the associated primes and the primary decomposition of this ideal, as well as its relation to initial ideals of lattice ideals.

When studying local properties of a polynomial ideal, one usually needs a theoretic technique called localization. For most cases, in spite of its importance, the computation in a localized ring cannot be algorithmically preformed. On the other hand, the standard basis method is very effective for the computation in a special kind of localized rings, but for a general semigroup order the geomet...

The j-multiplicity is an invariant that can be defined for any ideal in a Noetherian local ring (R, m). It is equal to the Hilbert-Samuel multiplicity if the ideal is m-primary. In this paper we explore the computability of the j-multiplicity, giving another proof for the length formula and the additive formula.

We provide methods to do explicit calculations in a polynomial ring in finitely many variables over a field. We develop algorithms to compute quotients of ideals, the radical of an ideal and a primary decomposition of an ideal. We also present methods to solve explicit tasks such as testing for prime ideals or identical ideals.

We define the notion of a power stable ideal in a polynomial ring R[X] over an integral domain R. It is proved that a maximal ideal χ M in R[X] is power stable if and only if P t is P primary for all t ≥ 1 for the prime ideal P = M ∩ R. Using this we prove that for a Hilbert domain R any radical ideal in R[X] which is a finite intersection G-ideals is power stable. Further, we prove that if R i...

in this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. in particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over noetherian rings are proved. moreover, w...