The patch topology and the ultrafilter topology on the prime spectrum of a commutative ring

Let R be a commutative ring and let Spec(R) denote the collection of prime ideals of R. We define a topology on Spec(R) by using ultrafilters and demonstrate that this topology is identical to the well known patch or constructible topology. The proof is accomplished by use of a von Neumann regular ring canonically associated with $R$.Comment: A Remark was added at the end of the paper. To appear in Comm. Algebr

Nagata Rings, Kronecker Function Rings and Related Semistar Operations

In 1994, Matsuda and Okabe introduced the notion of semistar operation. This concept extends the classical concept of star operation (cf. for instance, Gilmer's book \cite{G}) and, hence, the related classical theory of ideal systems based on the works by W. Krull, E. Noether, H. Pr\"{u}fer and P. Lorenzen from 1930's. In \cite{FL1} and \cite{FL2} the current authors investigated properties of the Kronecker function rings which arise from arbitrary semistar operations on an integral domain $D$. In this paper we extend that study and also generalize Kang's notion of a star Nagata ring \cite{Kang:1987} and \cite{Kang:1989} to the semistar setting. Our principal focuses are the similarities between the ideal structure of the Nagata and Kronecker semistar rings and between the natural semistar operations that these two types of function rings give rise to on $D$.Comment: 20 page

An historical overview of Kronecker function rings, Nagata rings, and related star and semistar operations

An historical overview of Kronecker function rings, Nagata rings, and related star and semistar operationsComment: "Multiplicative Ideal Theory in Commutative Algebra: A tribute to the work of Robert Gilmer", Jim Brewer, Sarah Glaz, William Heinzer, and Bruce Olberding Editors, Springer (to appear

Cancellation properties in ideal systems: A classification of e.a.b.\boldsymbol{e.a.b.} semistar operations

We give a classification of {\texttt{e.a.b.}} semistar (and star) operations by defining four different (successively smaller) distinguished classes. Then, using a standard notion of equivalence of semistar (and star) operations to partition the collection of all {\texttt{e.a.b.}} semistar (or star) operations, we show that there is exactly one operation of finite type in each equivalence class and that this operation has a range of nice properties. We give examples to demonstrate that the four classes of {\texttt{e.a.b.}} semistar (or star) operations we defined can all be distinct. In particular, we solve the open problem of showing that {\texttt{a.b.}} is really a stronger condition than {\texttt{e.a.b.}

Catastrophic volcanism as a cause of shocked features found at the K/T boundary and in cryptoexplosion structures

The presence of quartz grains containing shock lamellae at the Cretaceous/Tertiary (K/T) boundary is viewed by many as the single most compelling evidence of meteoritic or cometary impact because there is no known endogenous mechanism for producing these features. Similarly the presence of shocked quartz, shatter cones, coesite and stishovite at cryptoexplosion structures is comonly taken as conclusive evidence of impact. However, several recent studies have cast doubt on this interpretation. It is argued that basaltic volcanism, although not normally explosive, can under exceptional circumstances produce overpressures sufficiently high to produce shock features. The exceptional circumstances include a high content of volatiles, usually CO2, and no preestablished pathway to the surface. Rapid cooling of the saturated basaltic magma can occur if it underlies a cooler more evolved magma in a chamber. Initial slow cooling and partial exsolution of the volatiles will cause the density of the basaltic magma to become less than that of the overlying magma, leading to overturning and mixing. Gas will escape the magma chamber along planar cracks once the pressure becomes sufficiently high. In the vicinity of the crack tip there is a smallscale deviatoric stress pattern which is thought to be sufficiently high to produce transient cracks along secondary axes in the quartz crystals, causing the planar features. The CO2-rich fluid inclusions which have been found along planar elements of quartz in basement rocks of the Vredefort Dome were likely to have been emplaced by such a process. If the mechanism described is capable of producing shocked features as above, it would require a reassessment of the origin of many cryptoexplosion structures as well as seriously weakening the case for an impact origin of the K/T event

W v Registrar of Marriages and the right to equality in Hong Kong

This article contends that the Hong Kong government's decision to deny a transgender woman's application to marry her male partner, reviewed by the Court of First Instance in W v Registrar of Marriages, engages a right to equality and non-discrimination in Hong Kong constitutional law as well as anti-discrimination legislation. In light of the relative marginalization of the transgender community and Hong Kong's reasonably robust equality jurisprudence, framing W's challenge more explicitly on equality grounds may have had some advantages. In particular, a focus on equality may have strengthened the court's resolve to exercise its duty to protect the rights of minorities against discriminatory social attitudes.published_or_final_versio

The Rights to Self-determination: Recent Developments in International Law and Their Relevance for the Tibetan People

This article reviews developments in the understanding of a right to self-determination under international law in terms of the right's applicability and potential for resolving the Tibetan people's claims for self-government or independence. While a right to self-determination could likely justify Tibetan independence or secession from China, especially in light of continuing human rights abuses in Tibet, current political realities and global trends toward an expansion of ‘internal’ options for realising self-determination within existing states make secession unlikely. Less radical solutions, such as greater autonomy, federal political structures and an improved minority rights regime, could provide more realistic mechanisms for settling the Tibetan question. Successful resolution, however, ultimately depends on the level of genuine international concern as well as the extent to which the Chinese Government is willing to accept greater democratic participation and consider more flexible notions of state sovereignty and territorial integrity.published_or_final_versio

Equality and inclusion in education for persons with disabilities: Article 24 of the convention on the rights of persons with disabilities and its implementation in Hong Kong

Focus: Inclusion in Education for Persons with DisabilitiesThis article considers the extent to which a legal right to equality and nondiscrimination - as it has been expressed and developed in international law, domestic legislation and constitutional provisions - can support inclusion in education for persons with disabilities. Article 24 of the United Nations Convention on the Rights of Persons with Disabilities (CRPD) and other relevant human rights standards serve as reference points for this discussion. The article explores the concepts of disability (based on the social model), substantive equality, and inclusion and argues that these notions combine to form a theoretical foundation for a strong legal framework that requires transformative measures. It considers how these concepts are refl ected in international human rights law and how they have been applied in Hong Kong domestic law. It concludes that legal reforms are necessary for Hong Kong to fully implement its obligations to ensure inclusive education and substantive equality under the CRPD.published_or_final_versio