Journal article
When are Associates Unit Multiples?
The Rocky Mountain journal of mathematics, Vol.34(3), pp.811-828
09/2004
DOI: 10.1216/rmjm/1181069828
Abstract
Let R be a commutative ring with identity. For a, b ∈ R define a and b to be associates, denoted a ∼ b, if a∣b and b∣a, to be strong associates, denoted a ≈ b, if a = ub for some unit u of R, and to be very strong associates, denoted by a ≅ b, if a∼ b and further when a ≠ 0, a = rb implies that r is a unit. Certainly a ≅ b ⇒ a ≈ b ⇒ a ∼ b. In this paper we study commutative rings R, called strongly associate rings, with the property that for a, b ∈ R, a ∼ b implies a ≈ b and commutative rings R, called présimplifiable rings, with the property that for a, b ∈ R, a ∼ b (or a ≈ b) implies that a ≅ b.
Details
- Title: Subtitle
- When are Associates Unit Multiples?
- Creators
- D.D AndersonM AxtellS.J FormanJoe Stickles
- Resource Type
- Journal article
- Publication Details
- The Rocky Mountain journal of mathematics, Vol.34(3), pp.811-828
- DOI
- 10.1216/rmjm/1181069828
- ISSN
- 0035-7596
- eISSN
- 1945-3795
- Language
- English
- Date published
- 09/2004
- Academic Unit
- Mathematics
- Record Identifier
- 9983985940202771
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