On some factorial properties of subrings

Piotr Jędrzejewicz,

Łukasz Matysiak,

Janusz Zieliński

Abstrakt

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.

Słowa kluczowe: Irreducible element, square-free element, factorization, Jacobian Conjecture
References

1. Anderson D.F., Root closure in integral domains, J. Algebra, 79 (1982), 51–59.

2. Ayad M., Sur les polynˆomes f (X, Y ) tels que K [f ] est int´egralement ferm´e 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), 663–680.

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  the   “September School”  of  Algebraic   Geometry,aix1.uottawa.ca/~ddaigle/.L- ukec cin,   Poland,   September 2003 (unpublished),

7. Essen A. van den, Polynomial automorphisms and the Jacobian Conjecture, Birkh¨auser Verlag, Basel, 2000.

8. Freudenburg G., Algebraic theory of locally nilpotent derivations, Springer Verlag, Berlin, 2006.

9. Geroldinger A., Halter-Koch F., Non-unique factorizations, algebraic, combinatorial and analytic 

theory, Chapman & Hall/CRC, Boca Raton, 2006.

10. Jędrzejewicz  P., Rings of constants of p-homogeneous  polynomial derivations,  Comm. Algebra, 31 (2003), 5501–5511.

11. Jędrzejewicz P., Eigenvector p-bases of rings of constants of derivations, Comm. Algebra, 36 (2008), 1500–1508.

12. Jec drzejewicz P., One-element  p-bases of rings of constants of derivations, Osaka J. Math., 46 (2009), 223–234.

13. Jędrzejewicz P., A note on rings of constants of derivations in integral domains, Colloq. Math., 122 (2011), 241–245.

14. P. Jędrzejewicz , Positive characteristic analogs of closed polynomials, Cent. Eur. J. Math., 9 (2011), 50–56.

15. Jędrzejewicz  P., Jacobian conditions for p-bases, Comm. Algebra, 40 (2012), 2841–2852.

16. Jędrzejewicz  P., A characterization of Keller maps, J. Pure Appl. Algebra, 217 (2013), 165–171.

17. Jędrzejewicz  P., Zielin´ski 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 fields of constants for derivations in characteristic zero, J. Pure Appl. Algebra, 96 (1994), 47–55.

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