The algebra of one-sided inverses of polynomial algebra
نویسنده
چکیده
We study in detail the algebra Sn in the title which is an algebra obtained from a polynomial algebra Pn in n variables by adding commuting, left (but not two-sided) inverses of the canonical generators of Pn. The algebra Sn is non-commutative and neither left nor right Noetherian but the set of its ideals satisfies the a.c.c., and the ideals commute. It is proved that the classical Krull dimension of Sn is 2n; but the weak and the global dimensions of Sn are n. The prime and maximal spectra of Sn are found, and the simple Sn-modules are classified. It is proved that the algebra Sn is central, prime, and catenary. The set In of idempotent ideals of Sn is found explicitly, it is a distributive lattice.
منابع مشابه
The group K1(Sn) of the algebra of one-sided inverses of a polynomial algebra
The algebra Sn of one-sided inverses of a polynomial algebra Pn in n variables is obtained from Pn by adding commuting, left (but not two-sided) inverses of the canonical generators of the algebra Pn. The algebra Sn is a noncommutative, non-Noetherian algebra of classical Krull dimension 2n and of global dimension n and is not a domain. If the ground field K has characteristic zero then the alg...
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The algebra Sn of one-sided inverses of a polynomial algebra Pn in n variables is obtained from Pn by adding commuting, left (but not two-sided) inverses of the canonical generators of the algebra Pn. Ignoring non-Noetherian property, the algebra Sn belongs to a family of algebras like the nth Weyl algebra An and the polynomial algebra P2n. Explicit generators are found for the group Gn of auto...
متن کاملThe group of automorphisms of the algebra of one-sided inverses of a polynomial algebra
The algebra Sn in the title is obtained from a polynomial algebra Pn in n variables by adding commuting, left (but not two-sided) inverses of the canonical generators of Pn. Ignoring non-Noetherian property, the algebra Sn belongs to a family of algebras like the Weyl algebra An and the polynomial algebra P2n. The group of automorphisms Gn of the algebra Sn is found: Gn = Sn ⋉ T n ⋉ Inn(Sn) ⊇ S...
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