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The Keystone Exam is a Pennsylvania standardized test administered to the public schools of Pennsylvania, United States. The test has been developed by the Commonwealth of Pennsylvania Department of Education. Since the 2012–2013 school year, the General Keystone Knowledge Test Literature, Biology, and Algebra I VHS Exams have been available. [1]
Two-dimensional plot (red curve) of the algebraic equation . Elementary algebra, also known as college algebra, [1] encompasses the basic concepts of algebra. It is often contrasted with arithmetic: arithmetic deals with specified numbers, [2] whilst algebra introduces variables (quantities without fixed values). [3]
Algebra is the branch of mathematics that studies algebraic structures and the operations [a] they use. [2] An algebraic structure is a non-empty set of mathematical objects, such as the integers, together with algebraic operations defined on that set, like addition and multiplication. [3]
A graded module that is also a graded ring is called a graded algebra. A graded ring could also be viewed as a graded Z {\displaystyle \mathbb {Z} } -algebra. The associativity is not important (in fact not used at all) in the definition of a graded ring; hence, the notion applies to non-associative algebras as well; e.g., one can ...
Abstract algebra. The permutations of the Rubik's Cube form a group, a fundamental concept within abstract algebra. 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 ...
Algebra extension. In abstract algebra, an algebra extension is the ring-theoretic equivalent of a group extension. Precisely, a ring extension of a ring R by an abelian group I is a pair (E, ) consisting of a ring E and a ring homomorphism that fits into the short exact sequence of abelian groups: This makes I isomorphic to a two-sided ideal ...