Equational Noetherian Algebras and Chain Conditions
Equational Noetherian Algebras and Chain Conditions
In this article, we describe the relation between the properties of being equational noetherian and ascending chain condition on ideals of an arbitrary algebra. We also give a formulation of Hilbert's basis theorem for varieties of algebras and obtain a criterion to investigate it for a given variety.
8 pages
алгебраическое множество, уравнения, Zariski topol ogy, предмногообразие, max-n group, нетерова алгебра, equationally noetherian algebra, эквициональность нетеровых алгебр, Mathematics - Algebraic Geometry, теорема Гильберта о базисе, координатная алгебра, equations, FOS: Mathematics, максимальная n-группа, свободное произведение, Noetherain algebra, free product, алгебраические структуры, Algebraic Geometry (math.AG), pre-variety, algebraic set, Hilbert’s basis theorem, coordinate algebra, радикал, Mathematics - Logic, algebraic structures, топология Зарисского, variety, radical ideal, Primary 03C99, Secondary 08A99 and 14A99, многообразие, Zariski topology, noetherain algebra, Commutative Noetherian rings and modules, Logic (math.LO)
алгебраическое множество, уравнения, Zariski topol ogy, предмногообразие, max-n group, нетерова алгебра, equationally noetherian algebra, эквициональность нетеровых алгебр, Mathematics - Algebraic Geometry, теорема Гильберта о базисе, координатная алгебра, equations, FOS: Mathematics, максимальная n-группа, свободное произведение, Noetherain algebra, free product, алгебраические структуры, Algebraic Geometry (math.AG), pre-variety, algebraic set, Hilbert’s basis theorem, coordinate algebra, радикал, Mathematics - Logic, algebraic structures, топология Зарисского, variety, radical ideal, Primary 03C99, Secondary 08A99 and 14A99, многообразие, Zariski topology, noetherain algebra, Commutative Noetherian rings and modules, Logic (math.LO)
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