Algebra - vocabulary

Gaussian, adj.

Elimination, n. (created from a verb eliminate, /ᵻˈlɪmᵻneɪt/, and a suffix -ion)

Algorithm, n.

Pronounciation:

/ˈɡaʊsɪən/, /ᵻˌlɪmᵻˈneɪʃn/, /ˈalɡərɪð(ə)m/

Meaning:

Gaussian: Discovered or formulated by Gauss.

Elimination: The removal of a constant, variable, factor, etc., from a system of equations or a matrix by algebraic manipulation.

Algorithm: A procedure or set of rules used in calculation and problem-solving; (in later use spec.) a precisely defined set of mathematical or logical operations for the performance of a particular task.

Source:

OED

noun

pronunciation:

[ ˈgreytist ˈkämən diˈvīzər dōˈmān ]

meaning:

is an integral domain with the property that any two elements have a greatest common divisor (GCD)

property:

If R is a GCD domain, then the polynomial ring R[X₁,...,X_n] is also a GCD domain.

a set of operations so constituted that the product of any number of these operations is always itself a member of the set. In later use more generally: a set of elements together with an operation for combining any two of them to form a third element which is also in the set, the operation satisfying certain conditions.

Etymology:  French groupe, grouppe small detachment of soldiers (1574), arrangement of two or more figures or objects in a design . 1668), (in music) series of notes forming an ornament, run, etc., or linked by a slur (1703), number of things having some related properties or attributes in common (1726)

https://www.oed.com/

noun

pronunciation:

[ gro͞op ˌhōməˈmôrˌfizəm ]

meaning:

given two groups, (G, ∗) and (H, ·), a group homomorphism from (G, ∗) to (H, ·) is a function h : G → H such that for all u and v in G it holds that

where the group operation on the left hand side of the equation is that of G and on the right hand side that of H.

From this property, one can deduce that h maps the identity element e_G of G to the identity element e_H of H, 

and it also maps inverses to inverses in the sense that