This is my area of research, and I want to know everything that is new about it. You can send me your questions at zafrullah@lohar.com (or mithelp@lohar.com.) I will display them for everyone to see and comment. (Some questions are never asked because they occurred to a person who is shy, or is worried about the answer being common knowledge. Ask away the questions now. I will display your question, at your request, as anonymous. Once I know that the experts think your question is a valid question, and that answers to it will increase our knowledge content, I will include your name and address and invite you to make some comments on how to answer this question.) If your work is related to multiplicative ideal theory, and new, I want everyone to know about it. You can send me the title and abstract of your Ph D thesis (if you are a new Ph D), and you can send me the title, abstract and other relevant data of your upcoming or recently published paper. Whatever you send me will be displayed under a suitable heading for everyone to see. If you need to make an announcement about an upcoming conference or if you want to make a call for papers on multiplicative ideal theory, just send me the relevant material in a presentable form. I will display it.

Some Papers (Recent and Old)

Recent

Listed below are some of my recent paper and talks. Click on the highlighted part to get a pdf version of the preprint or talk.  Please remember, I am just a human. So, if you find some error /errors, in what I have put here, do please let me know at zafrullah@lohar.com. I would not hide my appreciation of this kindness, as some of you know. Here then are some articles, click away at what intrigues you or what you have not yet seen.

  1. Primes that become primal in a pullback, Internat. J. Comm. Ring Theory (to appear) (with T. Dumitrescu and N. Radu).
  2. The ring D+XD[1/S][X] and t-splitting sets, Arabian Journal for Science and Engineering, Vol 26 (1)(2001) to appear  (with D. D. Anderson and D.F. Anderson)
  3. Distinguished domains,  Internat. J. Comm. Ring Theory (to appear) (with D.D. Anderson and J. Kwak).
  4. LCM-splitting sets in some ring extensions Proc. Amer. Math. Soc.(to appear),(with T. Dumitrescu).
  5. Almost GCD domains of finite t-character, J. Algebra (to appear) (with T. Dumitrescu, Y. Lequain and J. Mott)
  6. Various Facets of Rings between D[X] and K[X]. (Survey Article ) Comm. Algebra (to appear).
  7. A Property of weakly Krull domains, Proc. Amer. Math. Soc.(to appear) (with D.D. Anderson).
  8. Almost splitting sets and AGCD domains, Comm. Algebra (to appear) (with D.D. Anderson and T. Dumitrescu)
  9. t-Splitting Sets in Integral Domains, J. Pure Appl. Algebra (to appear) (with G.W. Chang and T. Dumitrescu)
  10. A note on almost GCD monoids, Semigroup Forum( to appear) (with D.D. Anderson)
  11. Weakly Krull inside factorial domains, Proceedings of the Chapel Hill Conference (to appear) (with D. D. Anderson and G. W. Chang)
  12. UMV-domains, Proceedings of the Chapel Hill Conference (to appear) (with E.G. Houston)
  13. Factorization of certain sets of polynomials in an integral domain, Internat. J. Comm. Ring Theory (with D. D. Anderson and Pramod K. Sharma)  
  14. t-Splitting multiplicative sets of ideals in integral domains, J. Pure Appl. Algebra (to appear) (with G. W. Chang and T. Dumitrescu)
  15. Domains over which polynomials split (preprint)
  16. The w-integral closure of integral domains, with G. W. Chang (to appear in J. Algebra)
  17. The Schreier property and Gauss' Lemma, with D. D. Anderson (to appear)
  18. The half-factorial property and the domains of the form A+XB[X], with J. Coykendall and T. Dumitrescu (to appear in Houston J. Math.)
  19. What v-coprimality can do for you. A talk given at a workshop, on Commutative Rings and their Modules, held at Cortona, Italy in June 2004. 
  20. Quasi-Schreier domains II, Comm. Algebra (to appear) with D. D. Anderson and Tiberiu Dumitrescu 
  21. What v-coprimality can do for you, a survey article, to appear in " Multiplicative Ideal Theory in Commutative Algebra: A tribute to the work of Robert Gilmer", Jim Brewer, Sarah Glaz, William Heinzer, and Bruce Olberding Editors, Springer.
  22. Pseudo Almost Integral elements, Comm. Algebra (to appear) with D.D. Anderson
  23. Monoid Domain Constructions of antimatter domains, Comm. Algebra (to appear) with D.D. Anderson, J. Coykendall, and Linda Hill
  24. Factoriality in Riesz groups, with Joe L. Mott and Muneer A. Rashid (to appear in J. Group Theory)
  25. Unique Representation domains, II, with Said El Baghdadi and Stefania  Gabelli (to appear in J. Pure Appl. Algebra)
  26. Some remarks on Prufer *-multiplication domains and class groups, with David Anderson and Marco Fontana, (to appear in J. Algebra)
  27. A Question/Answer session on v-domain. A kind of survey on v-domains, that includes a bit of history (recent and old) of v-domains, some description of star operations and ideal systems and most of known results on v-domains. The mode is Question/Answer and relaxed. You can write to the author for more or to correct him or to suggest improvements.
  28. Almost Bezout domains, III (with Dan Anderson) to appear in Bull Math Soc Sci Math Roumanie.

Some important papers in Multiplicative Ideal Theory

Here are some classic papers whose authors have given me permission to put them on display. 

D. D. Anderson, Star-operations induced by overrings, Comm. Algebra 16(12)(1988) 2535-2553.

D.F. Anderson and D.E. Dobbs, Pairs of rings with the same prime ideals, Can. J. Math. 32(2)(1980) 362-384.

A. Bouvier,  Le groupe des classes d’un anneau integre, in « 107 eme Congres des Societes Savantes, Brest, (1982) Vol. 4, pp. 85-92.

P.M. Cohn, Bezout rings and their subrings, Proc. Cambridge Philos. Soc. 64(1968), 251-264. (This paper forged a new direction in the study of divisibility and factorization by introducing the notion of a Schreier domain as an integrally closed integral domain with group of divisibility a Riesz group.) Paul Cohn gave me a reprint and I am proud to have kept it since 1972 and read it. I must confess that I have just scratched the surface, there is much more to that paper than just Schreier domains. To see some of the effects of the Schreier domain part look up The Schreier property and Gauss' Lemma, (this paper incidentally has appeared: Bolletino U.M.I. 8 10-B (2007), 43-62.).) I could not get Paul’s permission to put this paper on my webpage, as I always thought I would get a good copy and then ask for his permission, it never occurred to me that he could die. In any case I wrote to Cambridge University Press, did not hear from them, except for an acknowledgment. Now I am putting it up with the intention that if there is an objection I would take down the paper and keep up the reference. The world is too technical for my taste.

J. Hedstrom and E. Houston, Some remarks on star operations, Journal of Pure and Applied Algebra, 18(1980) 37-44.

Isidore Fleischer, Abstract Prufer Ideal Theory, J. Algebra 115(2)(1988) 332-337 and Errata on two articles (J. Algebra 124(1989) 533.

Marco Fontana, Topologically defined classes of commutative rings, Ann. Mat. Pura Appl. 123(4) (1980), 331--355.

Marco Fontana and Salah Kabbaj, On the Krull and valuative dimension of D+XD_S [X] domains, J. Pure and Applied Algebra 63(1990), 231-245.

Laszlo Fuchs, Riesz Groups, Ann. Scoula Norm. Sup. Pisa 19(1965), 1-34. (I found this paper useful in the study of pre-Schreier domains. But this is not the only work that made me a “Fuchs’ fan”, when I was cutting my research teeth as an M.Sc. student, in the late sixties, at the University of the Punjab Lahore, I took frequent “bites” at “partially ordered algebraic systems”.

Some Old Papers (of which I have very few reprints, if any) 

On a result of Gilmer, J. London Math. Soc. (2)(1977), 19-20.

On finite conductor domains, Manuscripta Math. 24(1978), 191-204.

The construction D + XD_S [X], J. Algebra 53(2)(1978), 423-439 (with Douglas Costa and Joe Mott)

On Prufer v-multiplication domains, Manuscripta Math., 35(1981), 1-26 (with Joe Mott)

A general theory of almost factoriality, Manuscripta Math., 51(1985), 29-62. (The unpublished paper of mine cited as “The *-property” later appeared as: On a property of pre-Schreier domains)

The GCD property and quadratic polynomials, J. Math. 9(1986), 749-752 (with S.B. Malik and J.L. Mott).

On generalized Dedekind domains, Mathematika 33(1986), 285-296.

On a property of pre-Schreier domains, Comm. Algebra 15(1987), 1895-1920.

On some class groups of an integral domain, Bull. Soc. Math. Grece (N.S.) 29(1988), 45-59 (with A. Bouvier).

The D+XD[1/S][X] construction from GCD domains, J. Pure Appl. Algebra 50(1988), 93-107.

Ascending chain conditions and star operations, Comm. Algebra 17(6)(1989), 1523-1533.

Contents of polynomials and invertibility, Comm. Algebra 18(1990), 1569-1583.

Well behaved prime t-ideals, J. Pure Appl. Algebra (1990), 199-207

Almost Bezout domains, J. Algebra 142(2)(1991), 285-309 (with Dan Anderson)

On Riesz Groups , Manuscripta Math. 80(1993), 225-238.

t-invertibility and comparability,  Commutative Ring Theory (eds. P.-J. Cahen, D. Costa, M. Fontana and S.-E. Kabbaj), Marcel Dekker, New York, 1994, 141-150 (with R. Gilmer and J. Mott).

P.M. Cohn's completely primal elements Zero-Dimensional Commutative Rings (eds. D.F. Anderson and D. Dobbs) Marcel Dekker, New York, 1995, 115-123 (with D.D. Anderson).

Examples in Modern Algebra with which students can play,  Primus 6 No. 4, (1996), 351-354 (with T. Jackson).  

 

Last Updated: June 13, 2005