Webare nitely generated (respectively, nitely presented) if and only if their direct sum A= B Cis nitely generated (respectively, nitely presented). Finally, we consider associative … WebSuppose we have commutative, unitary rings A, B and a (unit preserving) homomorphism φ: A → B which makes B an A -algebra. Suppose also we have elements f 1, …, f n ∈ B which generate the unit ideal and such that B f i, namely the localisation of B with respect to f i, is a finitely generated A -algebra. Show that then B is a finitely ...
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WebOct 15, 2008 · The structure of a finitely presented monomial algebra K [X] / K [I] over a field K is described. Here X is a finitely generated free monoid and I is a prime ideal of X that is finitely generated. As an application, a new structural proof of the recent result of Bell and Pekcagliyan [J. Bell, P. Pekcagliyan, Primitivity of finitely presented monomial … WebSep 24, 2015 · Zelos Malum. 6,483 2 13 30. "Finitely generated" and "finitely presented" are certainly different for groups. The details are over my head (I am not a group theorist, hardly even a mathematician), but I have it on good hearsay that at one time the … flaxseed water
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WebApr 9, 2024 · A finitely presented algebra is defined by a pair where G is a finite set of "generators" et R is a finite set of pairs of terms built from the generators … WebThe first statement follows from the fact that a ring of finite type over a Noetherian ring is of finite presentation, see Algebra, Lemma 10.31.4. Suppose that $f$ is of finite type and … WebOct 22, 2013 · If C is a variety in the sense of universal algebra, then an object M ∈ C is called finitely generated if there are elements a 1, …, a n such that M = a 1, …, a n , where the right hand side is the smallest subobject of M containing the a 1, …, a n. This yields the usual notion when C = S e t, G r p, R − M o d, R − C A l g etc. N i ... flaxseed water microwave