Example. Let X be an algebraic projective irreducible surface over a field k and let P be a closed point of X , C ⊂ X be an irreducible curve such that P ∈ C . If X and C are smooth at P , then we let t ∈ OX,P be a local equation of C at P and u ∈ OX,P be such that u|C ∈ OC,P is a local parameter at P . Denote by C the ideal defining the curve C near P . Now we can introduce a two-dimensional l...

The distribution of ideal class groups of Fq(T, √ M(T )) is examined for degree-four monic polynomials M ∈ Fq[T ] when Fq is a finite field of characteristic greater than 3 with q ∈ [20000, 100000] or q ∈ [1020000, 1100000] and M is irreducible or has an irreducible cubic factor. Particular attention is paid to the distribution of the p-Sylow part of the class group, and these results agree wit...

We show that the maximal subgroup of the free profinite semigroup associated by Almeida to an irreducible sofic shift is a free profinite group, generalizing an earlier result of the second author for the case of the full shift (whose corresponding maximal subgroup is the maximal subgroup of the minimal ideal). A corresponding result is proved for certain relatively free profinite semigroups. W...

A binary clutter is the family of odd circuits of a binary matroid, that is, the family of circuits that intersect with odd cardinality a fixed given subset of elements. Let A denote the 0;1 matrix whose rows are the characteristic vectors of the odd circuits. A binary clutter is ideal if the polyhedron fx 0 : Ax 1g is integral. Examples of ideal binary clutters are st-paths, st-cuts, T -joins ...

A binary clutter is the family of odd circuits of a binary matroid, that is, the family of circuits that intersect with odd cardinality a fixed given subset of elements. Let A denote the 0;1 matrix whose rows are the characteristic vectors of the odd circuits. A binary clutter is ideal if the polyhedron fx 0 : Ax 1g is integral. Examples of ideal binary clutters are st-paths, st-cuts, T -joins ...

In this paper, we characterize both closed and strongly subobjects in the category of bounded uniform filter spaces introduce two notions closure operators which satisfy weakly hereditary, idempotent productive properties. We further each Tj (j= 0,1) using these examine that them form quotient-reflective subcategories spaces. Also, connected Finally, ultraconnected objects topological relations...

For a compact, orientable, irreducible, ∂-irreducible, and an-annular 3-manifold, it is shown there are only finitely many boundary slopes for incompressible ∂-incompressible surfaces of bounded Euler characteristic. We use normal surface theory the inverse relationship crushing triangulation along [8] that inflating an ideal [12] to introduce study boundary-efficient triangulations end-efficie...

We study the approachability ideal I[κ+] in the context of large cardinals and properties of the regular cardinals below a singular κ. As a guiding example consider the approachability ideal I[אω+1] assuming that אω is a strong limit. In this case we obtain that club many points in אω+1 of cofinality אn for some n > 1 are approachable assuming the joint reflection of countable families of stati...

Introduction: The squarer is an important circuit building block in square-and-multiply-based exponentiation and inversion circuits. When GF(2) elements are represented in a normal basis, squaring is simply a circular shift operation. Therefore, most previous works on squarers focused on other representations of GF(2) elements. For practical applications where values of n are often in the range...

We study the structure of 0-primitive near-rings and are able to answer an open question in the theory of minimal ideals in near-rings to the negative, namely if the heart of a zero symmetric subdirectly irreducible near-ring is subdirectly irreducible again. Also, we will be able to classify when a simple near-ring with an identity and containing a minimal left ideal is a Jacobson radical near...