Inert type extensions and related factorization properties

초록

An extension R S of commutative rings is strongly inert (respectively, inert) if for nonzero a,b S, ab R implies a,b R (respectively, there exists a unit u S with ua,u-1b R). We investigate strongly inert and inert extensions and various related extensions, where we either require the product ab to be nonzero or that a and b be nonzerodivisors. Special emphasis is given to the relationship between factorization properties of R and S. © 2023

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