What network is arbitrum one?

Could you please clarify for me what network Arbitrum operates on? I understand that Arbitrum is a popular scaling solution for Ethereum, but I'm not entirely clear on whether it's a separate blockchain network entirely or if it simply runs as a layer 2 solution on top of the Ethereum mainnet. Could you elaborate on the specifics of Arbitrum's network architecture and how it interacts with the Ethereum blockchain?