Generalizations of semicoprime preradicals

Ahmad Yousefian Darani, Hojjat Mostafanasab

Abstract


This article introduces the notions quasi-co-\(n\)-absorbing preradicals and semi-co-\(n\)-absorbing preradicals, generalizing the concept of semicoprime preradicals.  We study the concepts quasi-co-\(n\)-absorbing submodules and  semi-co-\(n\)-absorbing submodules and their relations with quasi-co-\(n\)-absorbing preradicals and semi-co-\(n\)-absorbing preradicals using the lattice structure of preradicals.


Keywords


lattice, preradical, quasi-co-$n$-absorbing, semi-co-$n$-absorbing

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References


D. F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39 (2011) 1646-1672.

A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc. 75 (2007) 417-429.

A. Badawi and A. Yousean Darani, On weakly 2-absorbing ideals of commutative rings, Houston J. Math. 39 (2013), 441-452.

L. Bican, P. Jambor, T. Kepka and P. Nemec, Preradicals, Comment. Math. Univ. Carolinae 15(1) (1974) 75-83.

L. Bican, T. Kepka, and P. Nemec, Rings, Modules and Preradicals (Marcel Dekker, New York, 1982).

A. I. Kashu, On partial inverse operations in the lattice of submodules. Bulet. A. S. M. Mathematica, 2(69) (2012) 59-73.

A. I. Kashu, On some operations in the lattice of submodules determined by preradicals, Bull. Acad. Stiinte Repub. Mold. Mat. 2(66) (2011) 5-16.

M. Luisa Galvao, Preradicals of associative algebras and their connections with preradicals of modules. Modules and Comodules. Trends in Mathematics. Birkhauser, (2008) 203-225.

H. Mostafanasab, E. Yetkin, U. Tekir and A. Yousean Darani, On 2-absorbing primary submodules of modules over commutative rings, An. St. Univ. Ovidius Constanta, to appear.

H. Mostafanasab and A. Yousean Darani, Quasi-n-absorbing and semi-nabsorbing preradicals, submitted.

F. Raggi, J. Rios, S. Gavito, H. Rincon and R. Fernandez-Alonso, Semicoprime preradicals, J. Algebra Appl. 11(6) (2012) 1250115 (12 pages).

F. Raggi, J. Rios, H. Rincon and R. Fernandez-Alonso, Basic preradicals and main injective modules, J. Algebra Appl. 8(1) (2009) 1-16.

F. Raggi, J. Rios, H. Rincon, R. Fernandez-Alonso and C. Signoret, Prime and irreducible preradicals, J. Algebra Appl. 4(4) (2005) 451-466.

F. Raggi, J. Rios, H. Rincon, R. Fernandez-Alonso and C. Signoret, Semiprime preradicals, Comm. Algebra 37 (2009) 2811-2822.

F. Raggi, J. Rios, H. Rincon, R. Fernandez-Alonso and C. Signoret, The lattice structure of preradicals, Comm. Algebra 30(3) (2002) 1533-1544.

F. Raggi, J. Rios, H. Rincon, R. Fernandez-Alonso and C. Signoret, The lattice structure of preradicals II: partitions, J. Algebra Appl. 1(2) (2002) 201-214.

F. Raggi, J. Rios, H. Rincon, R. Fernandez-Alonso and C. Signoret, The lattice structure of preradicals III: operators, J. Pure and Applied Algebra 190 (2004) 251-265.

F. Raggi, J. Rios and R. Wisbauer, Coprime preradicals and modules, J. Pure Appl. Algebra, 200 (2005) 51-69.

B. Stenstrom, Rings of Quotients, Die Grundlehren der Mathematischen Wissenschaften, Band 217 (Springer Verlag, Berlin, 1975).

D. K. Tutuncu, and Y. Kuratomi, On generalized epi-projective modules. Math. J. Okayama Univ., 52 (2010) 111-122.

R. Wisbauer, Foundations of Module and Ring Theory (Gordon and Breach, Philadelphia, 1991).

A. Yousean Darani, and H. Mostafanasab, Co-2-absorbing preradicals and submodules, J. Algebra Appl. 14(7) (2015) 1550113 (23 pages).

A. Yousean Darani and H. Mostafanasab, On 2-absorbing preradicals, J. Algebra Appl. 14(2) (2015) 1550017 (22 pages)

A. Yousean Darani and F. Soheilnia, 2-absorbing and weakly 2-absorbing submoduels, Thai J. Math. 9(3) (2011) 577-584.

A. Yousean Darani and F. Soheilnia, On n-absorbing submodules, Math. Comm., 17 (2012), 547-557.


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