### Some articles on *left ideal, left, left ideals, ideal, ideals*:

Divisible Group - Generalization

... zero-divisor, and some authors require that R is a domain.) For every principal

... zero-divisor, and some authors require that R is a domain.) For every principal

**left ideal**Ra, any homomorphism from Ra into M extends to a homomorphism from R into M ... module is also called principally injective module.) For every finitely generated**left ideal**L of R, any homomorphism from L into M extends to a homomorphism ... Since injective**left**modules extend homomorphisms from all**left ideals**to R, injective modules are clearly divisible in sense 2 and 3 ...Von Neumann Regular Ring - Facts

... The following statements are equivalent for the ring R R is von Neumann regular every principal

... The following statements are equivalent for the ring R R is von Neumann regular every principal

**left ideal**is generated by an idempotent every finitely generated**left ideal**is generated by an idempotent every ... every short exact sequence of**left**R-modules is pure exact The corresponding statements for right modules are also equivalent to R being von Neumann regular ... dimension 0 and is reduced Every localization of R at a maximal**ideal**is a field R is a subring of a product of fields closed under taking "weak inverses" of x∈R (the unique element y ...Algebra Over A Field - Basic Concepts - Subalgebras and Ideals

... A

... A

**left ideal**of a K-algebra is a linear subspace that has the property that any element of the subspace multiplied on the**left**by any element of the ... In symbols, we say that a subset L of a K-algebra A is a**left ideal**if for every x and y in L, z in A and c in K, we have the following three statements ... closed under scalar multiplication), 3) z · x is in L (L is closed under**left**multiplication by arbitrary elements) ...Matrix Ring - Structure

... There is a one-to-one correspondence between the two-sided

... There is a one-to-one correspondence between the two-sided

**ideals**of Mn(R) and the two-sided**ideals**of R ... Namely, for each**ideal**I of R, the set of all n×n matrices with entries in I is an**ideal**of Mn(R), and each**ideal**of Mn(R) arises in this way ... For n ≥ 2, not every**left ideal**or right**ideal**of Mn(R) arises by the previous construction from a**left ideal**or a right**ideal**in R ...Essential Extension

... submodule H of M, implies that As a special case, an essential

... submodule H of M, implies that As a special case, an essential

**left ideal**of R is a**left ideal**which is essential as a submodule of the**left**module RR ... The**left ideal**has non-zero intersection with any non-zero**left ideal**of R ... Analogously, and essential right**ideal**is exactly an essential submodule of the right R module RR ...### Famous quotes containing the words ideal and/or left:

“It is well worth the efforts of a lifetime to have attained knowledge which justifies an attack on the root of all evil—viz. the deadly atheism which asserts that because forms of evil have always existed in society, therefore they must always exist; and that the attainment of a high *ideal* is a hopeless chimera.”

—Elizabeth Blackwell (1821–1910)

“Cannon to right of them,

Cannon to *left* of them,

Cannon in front of them

Volleyed and thundered;”

—Alfred Tennyson (1809–1892)

Main Site Subjects

Related Phrases

Related Words