Geodesic
Algebraic properties of bi-polymatroidal ideals
Algebra i analiz, Tome 26 (2014) no. 6, pp. 69-77.

Voir la notice de l'article provenant de la source Math-Net.Ru

Classes of monomial ideals are considered in the polynomial ring in two sets of variables $R=K[X_1,\dots,X_n;Y_1,\dots,Y_m]$. Some algebraic properties of bi-polymatroidal ideals of $R$ are studied. More precisely, the behavior of the monomial localization of such ideals is investigated.
Keywords: bi-polymatroidal ideals, monomial localization. 
@article{AA_2014_26_6_a3,
     author = {M. La Barbiera},
     title = {Algebraic properties of bi-polymatroidal ideals},
     journal = {Algebra i analiz},
     pages = {69--77},
     publisher = {mathdoc},
     volume = {26},
     number = {6},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2014_26_6_a3/}
}
TY  - JOUR
AU  - M. La Barbiera
TI  - Algebraic properties of bi-polymatroidal ideals
JO  - Algebra i analiz
PY  - 2014
SP  - 69
EP  - 77
VL  - 26
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2014_26_6_a3/
LA  - en
ID  - AA_2014_26_6_a3
ER  - 
%0 Journal Article
%A M. La Barbiera
%T Algebraic properties of bi-polymatroidal ideals
%J Algebra i analiz
%D 2014
%P 69-77
%V 26
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2014_26_6_a3/
%G en
%F AA_2014_26_6_a3
M. La Barbiera. Algebraic properties of bi-polymatroidal ideals. Algebra i analiz, Tome 26 (2014) no. 6, pp. 69-77. http://geodesic.mathdoc.fr/item/AA_2014_26_6_a3/

[1] Bandari S., Herzog J., “Monomial localization and polymatroidal ideals”, Europian J. Combin., 34:4 (2013), 752–763 | DOI | MR | Zbl

[2] Conca A., Herzog J., “Castelnuovo–Mumford regularity of products of ideals”, Collect. Math., 54:2 (2003), 137–152 | MR | Zbl

[3] Herzog J., Hibi T., “Discrete polymatroids”, J. Algebraic Combin., 16:3 (2002), 239–268 | DOI | MR | Zbl

[4] Herzog J., Rauf A., Vladoiu M., “The stable set of associated prime ideals of a polymatroidal ideal”, J. Algebraic Combin., 37:2 (2013), 289–312 | DOI | MR | Zbl

[5] La Barbiera M., “Integral closure and normality of some classes of Veronese-type ideals”, Riv. Mat. Univ. Parma (7), 9 (2008), 31–47 | MR | Zbl

[6] La Barbiera M., “On a class of monomial ideals generated by $s$-sequences”, Math. Rep. (Bucur.), 12(62):3 (2010), 201–216 | MR | Zbl

[7] La Barbiera M., “On standard invariants of bi-polymatroidal ideals”, Algebra Colloq., 21:2 (2014), 267–274 | DOI | MR | Zbl

[8] La Barbiera M., “A note on unmixed ideals of Veronese bi-type”, Turkish J. Math., 37:1 (2013), 1–7 | MR | Zbl

[9] Sturmfels B., Gröebner bases and convex polytopes, Univ. Lecture Ser., 8, Amer. Math. Soc., Providence, RI, 1996 | MR | Zbl

[10] Villarreal R. H., Monomial algebras, Monogr. Textbooks Pure Appl. Math., 238, Marcel Dekker, Inc., New York, 2001 | MR | Zbl