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On the saturations of submodules
Let R ⊆ S be a ring extension, and let A be an R-submodule of S. The saturation of A (in S) by τ is set A[τ] = {x ∈ S : tx ∈ A for some t ∈ τ}, where τ is a multiplicative subset of R. We study properties of saturations of R-submodules of S. We use this notion of saturation to characterize star oper...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2018
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/188378 |
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| Summary: | Let R ⊆ S be a ring extension, and let A be an R-submodule of S. The saturation of A (in S) by τ is set A[τ] = {x ∈ S : tx ∈ A for some t ∈ τ}, where τ is a multiplicative subset of R. We study properties of saturations of R-submodules of S. We use this notion of saturation to characterize star operations ⋆ on ring extensions R ⊆ S satisfying the relation (A ∩ B)⋆ = A⋆ ∩ B⋆ whenever A and B are two R-submodules of S such that AS = BS = S. |
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