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Every vector space is a free module, [1] but, if the ring of the coefficients is not a division ring (not a field in the commutative case), then there exist non-free modules. Given any set S and ring R, there is a free R-module with basis S, which is called the free module on S or module of formal R-linear combinations of the elements of S.
Oxyanions (polyatomic anions containing oxygen) are named with -ite or -ate, for a lesser or greater quantity of oxygen, respectively. For example, NO − 2 is nitrite, while NO − 3 is nitrate. If four oxyanions are possible, the prefixes hypo-and per-are used: hypochlorite is ClO −, perchlorate is ClO − 4.
In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation.. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor.
For two elements a 1 + b 1 i + c 1 j + d 1 k and a 2 + b 2 i + c 2 j + d 2 k, their product, called the Hamilton product (a 1 + b 1 i + c 1 j + d 1 k) (a 2 + b 2 i + c 2 j + d 2 k), is determined by the products of the basis elements and the distributive law. The distributive law makes it possible to expand the product so that it is a sum of ...
In mathematics, a modular equation is an algebraic equation satisfied by moduli, [1] in the sense of moduli problems.That is, given a number of functions on a moduli space, a modular equation is an equation holding between them, or in other words an identity for moduli.
Use the extended Euclidean algorithm to compute k −1, the modular multiplicative inverse of k mod 2 w, where w is the number of bits in a word. This inverse will exist since the numbers are odd and the modulus has no odd factors. For each number in the list, multiply it by k −1 and take the least significant word of the result.
The cell on the left is going through mitosis and its chromosomes have condensed. Cell nucleus: A cell's information center, the cell nucleus is the most conspicuous organelle found in a eukaryotic cell. It houses the cell's chromosomes, and is the place where almost all DNA replication and RNA synthesis (transcription) occur.
Henrietta Lacks (born Loretta Pleasant; August 1, 1920 – October 4, 1951) [2] was an African-American woman [5] whose cancer cells are the source of the HeLa cell line, the first immortalized human cell line [B] and one of the most important cell lines in medical research. An immortalized cell line reproduces indefinitely under specific ...