January 9681 – Twelfth Council of Toledo: King Erwig of the Visigoths initiates a council in which he implements diverse measures against the Jews in Spain. 1127 – Jin–Song Wars: Invading Jurchen soldiers from the Jin dynasty besiege and sack Bianjing (Kaifeng), the capital of the Song dynasty of China, and abduct Emperor Qinzong of Song and others, ending the Northern Song dynasty. 1349 – The Jewish population of Basel, believed by the residents to be the cause of the ongoing Black Death, is rounded up and incinerated.
Field extensionIn mathematics, particularly in algebra, a field extension is a pair of fields such that the operations of K are those of L restricted to K. In this case, L is an extension field of K and K is a subfield of L. For example, under the usual notions of addition and multiplication, the complex numbers are an extension field of the real numbers; the real numbers are a subfield of the complex numbers. Field extensions are fundamental in algebraic number theory, and in the study of polynomial roots through Galois theory, and are widely used in algebraic geometry.
Field (mathematics)In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known fields are the field of rational numbers, the field of real numbers and the field of complex numbers.
JanuaryJanuary is the first month of the year in the Julian and Gregorian calendars and is also the first of seven months to have a length of 31 days. The first day of the month is known as New Year's Day. It is, on average, the coldest month of the year within most of the Northern Hemisphere (where it is the second month of winter) and the warmest month of the year within most of the Southern Hemisphere (where it is the second month of summer). In the Southern hemisphere, January is the seasonal equivalent of July in the Northern hemisphere and vice versa.
AACS encryption key controversyA controversy surrounding the AACS cryptographic key arose in April 2007 when the Motion Picture Association of America and the Advanced Access Content System Licensing Administrator, LLC (AACS LA) began issuing cease and desist letters to websites publishing a 128-bit (16-byte) number, represented in hexadecimal as 09 F9 11 02 9D 74 E3 5B D8 41 56 C5 63 56 88 C0 (commonly referred to as 09 F9), a cryptographic key for HD DVDs and Blu-ray Discs.
Cent (currency)The cent is a monetary unit of many national currencies that equals of the basic monetary unit. Etymologically, the word cent derives from the Latin centum meaning 'hundred'. The cent sign is commonly a simple minuscule (lower case) letter . In North America, the c is crossed by a diagonal stroke or a vertical line (depending on typeface), yielding the character . The United States one cent coin is generally known by the nickname "penny", alluding to the British coin and unit of that name.
Finitely generated moduleIn mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called a finite R-module, finite over R, or a module of finite type. Related concepts include finitely cogenerated modules, finitely presented modules, finitely related modules and coherent modules all of which are defined below. Over a Noetherian ring the concepts of finitely generated, finitely presented and coherent modules coincide.
Algebraic numberAn algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number, because it is a root of the polynomial x^2 − x − 1. That is, it is a value for x for which the polynomial evaluates to zero. As another example, the complex number is algebraic because it is a root of x^4 + 4. All integers and rational numbers are algebraic, as are all roots of integers.
ArgumentAn argument is a series of sentences, statements or propositions some of which are called premises and one is the conclusion. The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persuasion. Arguments are intended to determine or show the degree of truth or acceptability of another statement called a conclusion. Arguments can be studied from three main perspectives: the logical, the dialectical and the rhetorical perspective.
CentOSCentOS (ˈsɛntɒs, from Community Enterprise Operating System; also known as CentOS Linux) is a discontinued Linux distribution that provided a free and open-source community-supported computing platform, functionally compatible with its upstream source, Red Hat Enterprise Linux (RHEL). In January 2014, CentOS announced the official joining with Red Hat while staying independent from RHEL, under a new CentOS governing board. The first CentOS release in May 2004, numbered as CentOS version 2, was forked from RHEL version 2.
