On some factorial properties of subrings

Piotr Jędrzejewicz,

Łukasz Matysiak,

Janusz Zieliński

Abstract. We discuss various factorial properties of subrings as well as
properties involving irreducible elements and square-free elements, in particular
ones connected with Jacobian conditions.
1. Anderson D.F., Root closure in integral domains, J. Algebra, 79 (1982), 51{59.
2. Ayad M., Sur les polyn^omes f(X; Y ) tels que K[f] est integralement ferme dans K[X; Y ],
Acta Arith., 105 (2002), 9{28.
3. Belluce L.P., Di Niola A., Ferraioli A.R., Ideals of MV-semirings and MV-algebras, in:
G.L. Litvinov, S.N. Sergeev (eds), Tropical and idempotent mathematics and applications,
AMS, Providence, 2014.
4. Bondt M. de, Yan D., Irreducibility properties of Keller maps, Algebra Colloq., 23 (2016),
5. Brewer J.W., Costa D.L., McCrimmon K., Seminormality and root closure in polynomial
rings and algebraic curves, J. Algebra, 58 (1979), 217{226.
6. Daigle D., Locally nilpotent derivations, Lecture notes for the September
School" of Algebraic Geometry, Luk, ecin, Poland, September 2003 (unpublished),
7. Essen A. van den, Polynomial automorphisms and the Jacobian Conjecture, Birkhauser
Verlag, Basel, 2000.
8. Freudenburg G., Algebraic theory of locally nilpotent derivations, Springer Verlag, Berlin,
9. Geroldinger A., Halter-Koch F., Non-unique factorizations, algebraic, combinatorial and
analytic theory, Chapman & Hall/CRC, Boca Raton, 2006.
10. J, edrzejewicz P., Rings of constants of p-homogeneous polynomial derivations, Comm.
Algebra, 31 (2003), 5501{5511.
11. J, edrzejewicz P., Eigenvector p-bases of rings of constants of derivations, Comm. Algebra,
36 (2008), 1500{1508.
12. J, edrzejewicz P., One-element p-bases of rings of constants of derivations, Osaka J. Math.,
46 (2009), 223{234.
13. J, edrzejewicz P., A note on rings of constants of derivations in integral domains, Colloq.
Math., 122 (2011), 241{245.
14. P. J, edrzejewicz, Positive characteristic analogs of closed polynomials, Cent. Eur. J. Math.,
9 (2011), 50{56.
15. J, edrzejewicz P., Jacobian conditions for p-bases, Comm. Algebra, 40 (2012), 2841{2852.
16. J, edrzejewicz P., A characterization of Keller maps, J. Pure Appl. Algebra, 217 (2013),
17. J, edrzejewicz P., Zielinski J., Analogs of Jacobian conditions for subrings, to appear in J.
Pure Appl. Algebra, arXiv:1601.01508.
18. Nowicki A., Polynomial derivations and their rings of constants, Nicolaus Copernicus
University, Torun, 1994, www.mat.umk.pl/~anow/.
19. Nowicki A., Rings and elds of constants for derivations in characteristic zero, J. Pure
Appl. Algebra, 96 (1994), 47{55.

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