Algebras over a commutative ring, central structure maps, and algebra homomorphisms

Depends on

• Commutative ring
• Ring homomorphism: additive, multiplicative, and required to send $1$ to $1$

Used by

• A ring with finitely many ideals of zero intersection whose quotients are Noetherian rings is Noetherian Corollary
• Global functions on geometrically connected and geometrically reduced proper schemes Corollary
• A degree-one derivation need not square to zero Counterexample
• A Deligne kernel need not be one external tensor factor Counterexample
• A rank-one Hecke algebra with a perfect symmetrizing form and degenerate regular trace Counterexample
• The generic point of the affine line has no relative k-valued coordinate Counterexample
• The left-to-right exact equivalence need not preserve the identity Counterexample
• A group acting on a ring by automorphisms and its invariant subring Definition
• A one-vertex framed quiver variety and its Hecke correspondence Definition
• Arbitrary-level cyclotomic Hecke, Murphy cell and multipartition Schur modules Definition
• Associative graded algebras, bimodules, and internal shifts Definition
• Bialgebras and bialgebra maps Definition
• Bialgebras, counits and antipodes over a commutative ring Definition
• Blocks of a finite-dimensional algebra via primitive central idempotents Definition
• Cell data, multipartition dominance, and higher-cell ideals Definition
• Cellular bases and cell modules Definition
• Coefficient-complete fixed-carrier codifferential deformation Definition
• Coefficientwise formal associative deformations Definition
• Cohomological differential graded algebra Definition
• Commutative Hopf algebras over a field Definition
• Complex associative algebra with involution Definition
• Enveloping algebra and the bimodule–module dictionary Definition
• Finite Hecke specialization and its regular-trace determinant Definition
• Frobenius functionals and associative pairings Definition
• Frobenius objects and typed colored knowledgeable sewing data Definition
• General Poisson manifolds from bivector fields Definition
• Graded coalgebras, bialgebras and Hopf algebras over a commutative ring Definition
• Hochschild cochains, differential, and Gerstenhaber insertion bracket Definition
• Integral elements over a commutative ring and algebraic integers Definition
• Integral elements subalgebra of an arbitrary ring map Definition
• Modules over a Hall algebra are unital algebra representations Definition
• Quasi-bialgebras, quasi-antipodes, and quasi-Hopf algebras Definition
• Representations of unital associative algebras Definition
• Scalars, tensor powers, the empty tensor, opposite algebras and finite sums Definition
• Subalgebra generated by a subset, algebras of finite type, and module-finite algebras Definition
• Symmetrized product of an associative algebra Definition
• Temperley–Lieb planar diagram data and endomorphism modules Definition
• The abstract Temperley–Lieb generator presentation Definition
• The degenerate affine Hecke algebra Definition
• The dual convolution algebra and rational modules Definition

…and 55 more results.

Dependency tree · two levels

7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

• W. Li, Commutative Algebra, Lectures 9-10 (standard reference, not scraped)