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Tag Archives: ideals
Elementary Module Theory (I)
Modules can be likened to “vector spaces for rings”. To be specific, we shall see later that a vector space is precisely a module over a field (or in some cases, a division ring). This set of notes assumes the … Continue reading
Posted in Notes
Tagged generated submodules, ideals, left ideals, modules, rings, scalar multiplication, simple modules, submodules
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Introduction to Ring Theory (5)
Our first order of the day is to state the correspondence between the ideals and subrings of R/I and those of R. This is totally analogous to the case of groups. Theorem. Let I be an ideal of R. There are 1-1 … Continue reading
Posted in Notes
Tagged advanced, chinese remainder theorem, ideals, maximal ideals, prime ideals, ring theory, rings
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Introduction to Ring Theory (3)
Ideals and Ring Quotients Suppose I is a subgroup of (R, +). Since + is abelian, I is automatically a normal subgroup and we get the group quotient (R/I, +). One asks when we can define the product operation on R/I. To be specific, each … Continue reading
Posted in Notes
Tagged advanced, gaussian integers, generated ideals, ideals, principal ideals, ring quotients, ring theory
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Mathematics and Such 