AcidAn acid is a molecule or ion capable of either donating a proton (i.e. hydrogen ion, H+), known as a Brønsted–Lowry acid, or forming a covalent bond with an electron pair, known as a Lewis acid. The first category of acids are the proton donors, or Brønsted–Lowry acids. In the special case of aqueous solutions, proton donors form the hydronium ion H3O+ and are known as Arrhenius acids. Brønsted and Lowry generalized the Arrhenius theory to include non-aqueous solvents.
Spectrum of a ringIn commutative algebra, the prime spectrum (or simply the spectrum) of a ring R is the set of all prime ideals of R, and is usually denoted by ; in algebraic geometry it is simultaneously a topological space equipped with the sheaf of rings . For any ideal I of R, define to be the set of prime ideals containing I. We can put a topology on by defining the to be This topology is called the Zariski topology. A basis for the Zariski topology can be constructed as follows. For f ∈ R, define Df to be the set of prime ideals of R not containing f.
PhenolsIn organic chemistry, phenols, sometimes called phenolics, are a class of chemical compounds consisting of one or more hydroxyl groups (−OH) bonded directly to an aromatic hydrocarbon group. The simplest is phenol, C6H5OH. Phenolic compounds are classified as simple phenols or polyphenols based on the number of phenol units in the molecule. Phenols are both synthesized industrially and produced by plants and microorganisms. Phenols are more acidic than typical alcohols.
PhenolPhenol, or Benzenol, (also known as carbolic acid or phenolic acid) is an aromatic organic compound with the molecular formula . It is a white crystalline solid that is volatile. The molecule consists of a phenyl group () bonded to a hydroxy group (). Mildly acidic, it requires careful handling because it can cause chemical burns. Phenol was first extracted from coal tar, but today is produced on a large scale (about 7 million tonnes a year) from petroleum-derived feedstocks.
ElectrochemistryElectrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential difference as an outcome of a particular chemical change, or vice versa. These reactions involve electrons moving via an electronically-conducting phase (typically an external electrical circuit, but not necessarily, as in electroless plating) between electrodes separated by an ionically conducting and electronically insulating electrolyte (or ionic species in a solution).
Completion of a ringIn abstract algebra, a completion is any of several related functors on rings and modules that result in complete topological rings and modules. Completion is similar to localization, and together they are among the most basic tools in analysing commutative rings. Complete commutative rings have a simpler structure than general ones, and Hensel's lemma applies to them. In algebraic geometry, a completion of a ring of functions R on a space X concentrates on a formal neighborhood of a point of X: heuristically, this is a neighborhood so small that all Taylor series centered at the point are convergent.
Ringed spaceIn mathematics, a ringed space is a family of (commutative) rings parametrized by open subsets of a topological space together with ring homomorphisms that play roles of restrictions. Precisely, it is a topological space equipped with a sheaf of rings called a structure sheaf. It is an abstraction of the concept of the rings of continuous (scalar-valued) functions on open subsets. Among ringed spaces, especially important and prominent is a locally ringed space: a ringed space in which the analogy between the stalk at a point and the ring of germs of functions at a point is valid.
Reaction mechanismIn chemistry, a reaction mechanism is the step by step sequence of elementary reactions by which overall chemical reaction occurs. A chemical mechanism is a theoretical conjecture that tries to describe in detail what takes place at each stage of an overall chemical reaction. The detailed steps of a reaction are not observable in most cases. The conjectured mechanism is chosen because it is thermodynamically feasible and has experimental support in isolated intermediates (see next section) or other quantitative and qualitative characteristics of the reaction.
Group ringIn algebra, a group ring is a free module and at the same time a ring, constructed in a natural way from any given ring and any given group. As a free module, its ring of scalars is the given ring, and its basis is the set of elements of the given group. As a ring, its addition law is that of the free module and its multiplication extends "by linearity" the given group law on the basis. Less formally, a group ring is a generalization of a given group, by attaching to each element of the group a "weighting factor" from a given ring.
Consumption (economics)Consumption is the act of using resources to satisfy current needs and wants. It is seen in contrast to investing, which is spending for acquisition of future income. Consumption is a major concept in economics and is also studied in many other social sciences. Different schools of economists define consumption differently. According to mainstream economists, only the final purchase of newly produced goods and services by individuals for immediate use constitutes consumption, while other types of expenditure — in particular, fixed investment, intermediate consumption, and government spending — are placed in separate categories (see consumer choice).
