Search results
Results From The WOW.Com Content Network
A right R-module M R is defined similarly in terms of an operation · : M × R → M. Authors who do not require rings to be unital omit condition 4 in the definition above; they would call the structures defined above "unital left R-modules". In this article, consistent with the glossary of ring theory, all rings and modules are assumed to be ...
[2] On a local ring every finitely generated flat module is free. [3] A finitely generated flat module that is not projective can be built as follows. Let = be the set of the infinite sequences whose terms belong to a fixed field F. It is a commutative ring with addition and multiplication defined componentwise.
In 2015, educational psychologist Jonathan Wai of Duke University analyzed average test scores from the Army General Classification Test in 1946 (10,000 students), the Selective Service College Qualification Test in 1952 (38,420), Project Talent in the early 1970s (400,000), the Graduate Record Examination between 2002 and 2005 (over 1.2 ...
In mathematics, a sequence is an ... (A, R, M, Y). Also, the sequence (1, 1, 2, 3, 5, 8), which contains the number 1 at two different positions, is a valid sequence ...
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, and more specifically in homological algebra, a resolution (or left resolution; dually a coresolution or right resolution [1]) is an exact sequence of modules (or, more generally, of objects of an abelian category) that is used to define invariants characterizing the structure of a specific module or object of this category.
For example, taking the prime n = 2 results in the above-mentioned field F 2. For n = 4 and more generally, for any composite number (i.e., any number n which can be expressed as a product n = r ⋅ s of two strictly smaller natural numbers), Z / n Z is not a field: the product of two non-zero elements is zero since r ⋅ s = 0 in Z / n Z ...
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations acting on their elements. [1] Algebraic structures include groups , rings , fields , modules , vector spaces , lattices , and algebras over a field .