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- W81917145 abstract "Anderson and Frazier [6] defined a generalization of factorization in integral domains called τ -factorization. If D is an integral domain and τ is a symmetric relation on the nonzero nonunits of D, then a τ -factorization of a nonzero nonunit a ∈ D is an expression a = λa1 · · · an, where λ is a unit in D, each ai is a nonzero nonunit in D, and aiτaj for i 6= j. If τ = D ×D, where D denotes the nonzero nonunits of D, then the τ -factorizations are just the usual factorizations, and with other choices of τ we get interesting variants on standard factorization. For example, if we define aτdb ⇔ (a, b) = D, then the τd-factorizations are the comaximal factorizations introduced by McAdam and Swan [19]. Anderson and Frazier defined τ -factorization analogues of many different factorization concepts and properties, and proved a number of theorems either generalizing standard factorization results or the comaximal factorization results of McAdam and Swan. Some of these concepts include τ -UFD’s, τ -atomic domains, the τ -ACCP property, τ -BFD’s, τ -FFD’s, and τ -HFD’s. They showed the implications between these concepts and showed how each of the standard variations implied their τ -factorization counterparts (sometimes assuming certain natural constraints on τ). Later, Ortiz-Albino [21] introduced a new concept called Γ-factorization that generalized τ -factorization. We will summarize the known theory of τ -factorization and Γ-factorization as well as introduce several new or improved results." @default.
- W81917145 created "2016-06-24" @default.
- W81917145 creator A5034228887 @default.
- W81917145 date "2018-11-29" @default.
- W81917145 modified "2023-10-11" @default.
- W81917145 title "Some topics in abstract factorization" @default.
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- W81917145 doi "https://doi.org/10.17077/etd.5mkkf904" @default.
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