“Augmentation (algebra)”的意思、由来-开放百科全书

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Augmentation (algebra)

释义

References

In algebra, an augmentation of an associative algebra A over a commutative ring k is a k-algebra homomorphism , typically denoted by ε. An algebra together with an augmentation is called an augmented algebra. The kernel of the augmentation is a two-sided ideal called the augmentation ideal of A.

For example, if is the group algebra of a finite group G, then

is an augmentation.

If A is a graded algebra which is connected, i.e. , then the homomorphism which maps an element to its homogeneous component of degree 0 is an augmentation. For example,

is an augmentation on the polynomial ring .

References

{{cite book | last1=Loday | first1=Jean-Louis | authorlink1=Jean-Louis Loday | last2=Vallette | first2=Bruno | title=Algebraic operads | zbl=1260.18001 | series=Grundlehren der Mathematischen Wissenschaften | volume=346 | location=Berlin | publisher=Springer-Verlag | isbn=978-3-642-30361-6 | year=2012 | page=2 }}

1 : Algebras

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