You are here

A Note on Prüfer ⋆-multiplication Domains II

Journal Name:

Publication Year:

Abstract (2. Language): 
We bring some corrections to Corollary 1 of [3]. In [3], we attempted to show that for an arbitrary star operation ⋆ on a domain R, the domain R is a Prüfer ⋆-multiplication domain if and only if (a) ∩ (b) is ⋆f -invertible for all a, b ∈ R \ {0}. We show in this paper that the characterization does not hold in general and we restate [3, Corollary 1] with justification and proof as follows: if a domain R is a Prüfer ⋆-multiplication domain, then (a) ∩ (b) is ⋆f -invertible for all a, b ∈ R \ {0}. The converse holds only if ⋆f = t.
1
2

REFERENCES

References: 

[1] D.D. Anderson and D.F. Anderson. Generalized GCD domains, Commentarii Mathematici
Universitatis Sancti Pauli, 28, 215-221, 1979.
[2] D. D. Anderson, D. F. Anderson, M. Fontana, and M. Zafrullah. On v-Domains and Star
Operations. Communications in Algebra, 2: 141-145, 2008.
[3] O.A. Heubo-Kwegna. A note on Prüfer ⋆-multiplication domains, European Journal of Pure
and Applied Mathematics, 8(4): 458-461, 2015.
[4] M. Zafrullah. Putting t-invertibility to use, Non-Noetherian commutative ring theory, 429–
457, Mathematics and its Applications, 520, Kluwer Acad. Publ., Dordrecht, 2000.
[5] M. Zafrullah. t-invertibility and Bazzoni-like statements, Journal of Pure and Applied Alge-
bra, 214: 654-657, 2010.

Thank you for copying data from http://www.arastirmax.com