RELATIONSHIP BETWEEN WEAK ENTWINING STRUCTURES AND WEAK CORINGS - Diponegoro University | Institutional Repository (UNDIP-IR)

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Abstract. Given a commutative ring

A

and coalgebra

structure if only if

with unit,

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,

R -algebra A

and

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C

we can consider

A ⊗R C

is a

A ⊗R C

as a left

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R -coalgebra C.

R -linear map ψ : C ⊗R A → A ⊗R C

entwining structure if there is
algebra

R

++

"

( A, C ,ψ )

Triple

is called (weak)

that fulfil some axioms. In the other hand, from

A -module canonically such that ( A, C ,ψ )

A -coring. In particular, we obtain that ( A, C ,ψ )

is entwined

is a weak entwined structure if only if

A⊗ C

is a weak A -coring.
R
Keywords : algebra, coalgebra, coring, entwining structure.

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α : ( A ⊗R C ) ⊗R A → A ⊗R C , α ( ( a ⊗ b ) ⊗ c ) = aψ ( c ⊗ b ) , A ⊗R C
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∆ := I A ⊗ ∆ : A ⊗R C → A ⊗R C ⊗R C

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( A, C ,ψ )

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( A ⊗ R C ) ⊗ A ( A ⊗R C ) ,

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ε := I A ⊗ ε : A ⊗R C → A.
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