Geodesic
Uniformly $2$-absorbing primary ideals of commutative rings
Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 221-240.

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

In this study, we introduce the concept of "uniformly $2$-absorbing primary ideals" of commutative rings, which imposes a certain boundedness condition on the usual notion of $2$-absorbing primary ideals of commutative rings. Then we investigate some properties of uniformly $2$-absorbing primary ideals of commutative rings with examples. Also, we investigate a specific kind of uniformly $2$-absorbing primary ideals by the name of "special $2$-absorbing primary ideals".
Keywords: uniformly $2$-absorbing primary ideal, Noether strongly $2$-absorbing primary ideal, $2$-absorbing primary ideal. 
@article{ADM_2020_29_2_a7,
     author = {H. Mostafanasab and \"U. Tekir and G. Ulucak},
     title = {Uniformly $2$-absorbing primary ideals of commutative rings},
     journal = {Algebra and discrete mathematics},
     pages = {221--240},
     publisher = {mathdoc},
     volume = {29},
     number = {2},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a7/}
}
TY  - JOUR
AU  - H. Mostafanasab
AU  - Ü. Tekir
AU  - G. Ulucak
TI  - Uniformly $2$-absorbing primary ideals of commutative rings
JO  - Algebra and discrete mathematics
PY  - 2020
SP  - 221
EP  - 240
VL  - 29
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a7/
LA  - en
ID  - ADM_2020_29_2_a7
ER  - 
%0 Journal Article
%A H. Mostafanasab
%A Ü. Tekir
%A G. Ulucak
%T Uniformly $2$-absorbing primary ideals of commutative rings
%J Algebra and discrete mathematics
%D 2020
%P 221-240
%V 29
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a7/
%G en
%F ADM_2020_29_2_a7
H. Mostafanasab; Ü. Tekir; G. Ulucak. Uniformly $2$-absorbing primary ideals of commutative rings. Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 221-240. http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a7/

[1] D. F. Anderson and A. Badawi, “On $n$-absorbing ideals of commutative rings”, Comm. Algebra, 39 (2011), 1646–1672

[2] D. D. Anderson, K. R. Knopp and R. L. Lewin, “Ideals generated by powers of elements”, Bull. Austral. Math. Soc., 49 (1994), 373–376

[3] A. Badawi, “On $2$-absorbing ideals of commutative rings”, Bull. Austral. Math. Soc., 75 (2007), 417–429

[4] A. Badawi, Ü. Tekir and E. Yetkin, “On $2$-absorbing primary ideals in commutative rings”, Bull. Korean Math. Soc., 51:4 (2014), 1163–1173

[5] A. Badawi and A. Yousefian Darani, “On weakly $2$-absorbing ideals of commutative rings”, Houston J. Math., 39 (2013), 441–452

[6] J. A. Cox and A. J. Hetzel, “Uniformly primary ideals”, J. Pure Appl. Algebra, 212 (2008), 1–8

[7] M. Hochster, “Criteria for equality of ordinary and symbolic powers of primes”, Math. Z., 133 (1973), 53–65

[8] J. Hukaba, Commutative rings with zero divisors, Marcel Dekker, Inc., New York, 1988

[9] H. Mostafanasab, E. Yetkin, U. Tekir and A. Yousefian Darani, “On $2$-absorbing primary submodules of modules over commutative rings”, An. Şt. Univ. Ovidius Constanta, in press

[10] P. Nasehpour, On the Anderson-Badawi $\omega_{R[X]}(I[X])=\omega_R(I)$ conjecture, 2014, arXiv: arXiv:1401.0459

[11] D. G. Northcott, “A generalization of a theorem on the content of polynomials”, Proc. Cambridge Phil. Soc., 55 (1959), 282–288

[12] J. Ohm and D. E. Rush, “Content modules and algebras”, Math. Scand., 31 (1972), 49–68

[13] D. E. Rush, “Content algebras”, Canad. Math. Bull., 21:3 (1978), 329–334

[14] R. Y. Sharp, Steps in commutative algebra, 2nd. ed., Cambridge University Press, Cambridge, 2000

[15] A. Yousefian Darani and F. Soheilnia, “$2$-absorbing and weakly $2$-absorbing submoduels”, Thai J. Math., 9:3 (2011), 577–584

[16] A. Yousefian Darani and F. Soheilnia, “On $n$-absorbing submodules”, Math. Comm., 17 (2012), 547–557