ABSORBING MULTIPLICATION MODULES OVER PULLBACK RINGS

Year 2017, Volume: 21 Issue: 21, 76 - 90, 17.01.2017

S. Ebrahimi Atani , M. Sedghi Shanbeh Bazari

https://doi.org/10.24330/ieja.296034

Cited By: 1

https://izlik.org/JA97FG85ME

Abstract

Following some ideas and a technique introduced in [Comm. Algebra
41 (2013), pp. 776-791] we give a complete classification, up to isomorphism,
of all indecomposable 2-absorbing multiplication modules with finitedimensional
top over pullback of two discrete valuation domains with the same
residue field.

Keywords

Pullback , separated , non-separated , 2-absorbing multiplication module

References

• [1] D. M. Arnold and R. C. Laubenbacher, Finitely generated modules over pullback
• rings, J. Algebra, 184(1) (1996), 304-332.
• [2] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math.
• Soc., 75(3) (2007), 417-429.
• [3] A. Badawi, U. Tekir and E. Yetkin, On 2-absorbing primary ideals in commutative
• rings, Bull. Korean Math. Soc., 51(4) (2014), 1163-1173.
• [4] A. Badawi, U. Tekir and E. Yetkin, On weakly 2-absorbing primary ideals of
• commutative rings, J. Korean Math. Soc., 52(1) (2015), 97-111.
• [6] Ju. A. Drozd, Matrix problems and categories of matrices, In: Zap. Nauchn.
• Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 28 (1972), 144-153 (in
• Russian).
• [7] S. Ebrahimi Atani, On pure-injective modules over pullback rings, Comm. Algebra,
• 28(9) (2000), 4037-4069.
• [8] S. Ebrahimi Atani, On secondary modules over Dedekind domains, Southeast
• Asian Bull. Math, 25(1) (2001), 1-6.
• [9] S. Ebrahimi Atani, On secondary modules over pullback rings, Comm. Algebra,
• 30(6) (2002), 2675-2685.