A prime strongly positive amphicheiral knot which is not slice

A Prime Strongly Positive Amphicheiral Knot Which Is Not Slice

Infinite Order Amphicheiral Knots

In 1977 Gordon [G] asked whether every class of order two in the classical knot concordance group can be represented by an amphicheiral knot. The question remains open although counterexamples in higher dimensions are now known to exist [CM]. This problem is more naturally stated in terms of negative amphicheiral knots, since such knots represent 2–torsion in concordance; that is, if K is negat...

The Dual of a Strongly Prime Ideal

Let R be a commutative integral domain with quotient field K and let P be a nonzero strongly prime ideal of R. We give several characterizations of such ideals. It is shown that (P : P) is a valuation domain with the unique maximal ideal P. We also study when P^{&minus1} is a ring. In fact, it is proved that P^{&minus1} = (P : P) if and only if P is not invertible. Furthermore, if P is invertib...

SOME RESULTS ON STRONGLY PRIME SUBMODULES

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)ysubseteq P$ for $x, yin M$, implies that $xin P$ or $yin P$. In this paper, we study more properties of strongly prime submodules. It is shown that a finitely generated $R$-module $M$ is Artinian if and only if $M$ is Noetherian and every st...

Knot Groups and Slice Conditions

We introduce the notions of “k-connected-slice” and “π1-slice”, interpolating between “homotopy ribbon” and “slice”. We show that every high-dimensional knot group π is the group of an (n− 1)-connected-slice n-knot for all n ≥ 3. However if π is the group of an n-connected-slice n-knot the augmentation ideal I(π) must have deficiency 1 as a module. If moreover n = 2 and π is finitely generated ...