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Mostafanasab, Hojjat; Darani, Ahmad Yousefian

Quasi-\(n\)-absorbing and semi-\(n\)-absorbing preradicals. (English) Zbl 1488.16082

Hacet. J. Math. Stat. 48, No. 5, 1286-1303 (2019).
Summary: The aim of this paper is to introduce the notions of quasi-\(n\)-absorbing preradicals and of semi-\(n\)-absorbing preradicals. These notions are inspired by applying the concept of \(n\)-absorbing preradicals to semiprime preradicals. Also, we study the concepts of quasi-\(n\)-absorbing submodules and of semi-\(n\)-absorbing submodules and their relations with quasi-\(n\)-absorbing preradicals and semi-\(n\)-absorbing preradicals.

MSC:

16S90 Torsion theories; radicals on module categories (associative algebraic aspects)
06C05 Modular lattices, Desarguesian lattices
16N20 Jacobson radical, quasimultiplication

Keywords:

lattice; preradical; quasi-\(n\)-absorbing; semi-\(n\)-absorbing
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References:

[1] [1] D.F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39, 1646-1672, 2011. · Zbl 1232.13001
[2] [2] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75, 417-429, 2007. · Zbl 1120.13004
[3] [3] J. Beachy, M-injective modules and prime M-ideals, Comm. Algebra 30 (10), 4649- 4676, 2002. · Zbl 1058.16003
[4] [4] L. Bican, P. Jambor, T. Kepka and P. Nemec, Preradicals, Comment. Math. Univ. Carolinae 15 (1), 75-83, 1974. · Zbl 0277.16020
[5] [5] L. Bican, P. Jambor, T. Kepka and P. Nemec, Prime and coprime modules, Fund. Math. 107, 33-45, 1980. · Zbl 0354.16013
[6] [6] L. Bican, T. Kepka, and P. Nemec, Rings, Modules and Preradicals, Marcel Dekker, New York, 1982. · Zbl 0483.16026
[7] [7] A.I. Kashu, On some operations in the lattice of submodules determined by preradi- cals, Bull. Acad. Stiinte Repub. Mold. Mat. 2 (66), 5-16, 2011. · Zbl 1248.16006
[8] [8] T.Y. Lam, Lectures on Modules and Rings, Graduate Texts in Mathematics, Springer-Verlag, 1998.
[9] [9] F. Raggi, J. Ríos, H. Rincón and R. Fernández-Alonso, Basic preradicals and main injective modules, J. Algebra Appl. 8 (1), 1-16, 2009. · Zbl 1178.16017
[10] [10] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, The lattice structure of preradicals, Comm. Algebra 30 (3), 1533-1544, 2002. · Zbl 1007.16022
[11] [11] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, The lattice structure of preradicals II : partitions, J. Algebra Appl. 1 (2), 201-214, 2002. · Zbl 1034.16035
[12] [12] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, The lattice structure of preradicals III : operators, J. Pure and Applied Algebra 190, 251-265, 2004. · Zbl 1058.16030
[13] [13] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, Prime and irreducible preradicals, J. Algebra Appl. 4 (4), 451-466, 2005. · Zbl 1082.16027
[14] [14] F. Raggi, J. Ríos, H. Rincón, R. Fernández-Alonso and C. Signoret, Semiprime preradicals, Comm. Algebra 37, 2811-2822, 2009. · Zbl 1179.16006
[15] [15] B. Stenström, Rings of Quotients, Die Grundlehren der Mathematischen Wis- senschaften, Band 217, Springer Verlag, Berlin, 1975. · Zbl 0296.16001
[16] [16] D. Keskin Tütüncü and Y. Kuratomi, On mono-injective modules and mono-ojective modules, Math. J. Okayama Univ. 55, 117-129, 2013. · Zbl 1286.16005
[17] [17] R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia, 1991. · Zbl 0746.16001
[18] [18] A. Yousefian Darani, and H. Mostafanasab, Co-2-absorbing preradicals and submod- ules, J. Algebra Appl. 14 (7), 1550113 (23 pages), 2015. · Zbl 1326.16015
[19] [19] A. Yousefian Darani and H. Mostafanasab, On 2-absorbing preradicals, J. Algebra Appl. 14 (2), 1550017 (22 pages), 2015. · Zbl 1316.16015
[20] [20] A. Yousefian Darani and F. Soheilnia, 2-absorbing and weakly 2-absorbing submod- uels, Thai J. Math. 9 (3), 577-584, 2011. · Zbl 1277.13004
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