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Forcing linearity numbers for coatomic modules

Year 2018, Volume: 1 Issue: 1, 1 - 4, 30.09.2018
https://doi.org/10.33434/cams.446020

Abstract

We show that an integer $ n\in \mathbb{N}\cup \lbrace 0 \rbrace $ is the forcing linearity number of a coatomic module over an arbitrary commutative ring with identity if and only if $n\in \left\{ 0,1,2,\infty \right\} \cup \left\{ q+2\left\vert q\text{ is a prime power}\right. \right\} .$

References

  • [1] C.Faith, Algebra. II. Ring theory. Grundlehren der Mathematischen Wissenschaften, No. 191. Springer- Verlag, Berlin- New York, 1976.
  • [2] R.M.Hamsher, Commutative rings over which every module has a maximal submodule, Proc. Amer. Math. Soc. 18 (1967), 1133- 1137.
  • [3] C.J.Maxson, J.H.Meyer, Forcing linearity numbers, J.Algebra 223 (2000), 190- 207.
  • [4] C.J.Maxson, A.B.Van der Merwe, Forcing linearity numbers for modules over rings with nontrivial idempotents, J.Algebra 256 (2002), 66- 84.
  • [5] C.J.Maxson, A.B.Van der Merwe, Forcing linearity numbers for finitely generated modules, Rocky Mountain J.Math. 35 (3) (2005), 929-939.
  • [6] A.A.Tuganbaev, Rings whose nonzero modules have maximal submodules, J.Math.Sci. (New York) 109 (2002), no.3, 1589- 1640.
  • [7] H. Zöschinger, Koatomare Moduln, Math. Z. 170 (1980), 221- 232.
Year 2018, Volume: 1 Issue: 1, 1 - 4, 30.09.2018
https://doi.org/10.33434/cams.446020

Abstract

References

  • [1] C.Faith, Algebra. II. Ring theory. Grundlehren der Mathematischen Wissenschaften, No. 191. Springer- Verlag, Berlin- New York, 1976.
  • [2] R.M.Hamsher, Commutative rings over which every module has a maximal submodule, Proc. Amer. Math. Soc. 18 (1967), 1133- 1137.
  • [3] C.J.Maxson, J.H.Meyer, Forcing linearity numbers, J.Algebra 223 (2000), 190- 207.
  • [4] C.J.Maxson, A.B.Van der Merwe, Forcing linearity numbers for modules over rings with nontrivial idempotents, J.Algebra 256 (2002), 66- 84.
  • [5] C.J.Maxson, A.B.Van der Merwe, Forcing linearity numbers for finitely generated modules, Rocky Mountain J.Math. 35 (3) (2005), 929-939.
  • [6] A.A.Tuganbaev, Rings whose nonzero modules have maximal submodules, J.Math.Sci. (New York) 109 (2002), no.3, 1589- 1640.
  • [7] H. Zöschinger, Koatomare Moduln, Math. Z. 170 (1980), 221- 232.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Peter R. Fuchs 0000-0001-9165-3688

Publication Date September 30, 2018
Submission Date July 19, 2018
Acceptance Date September 19, 2018
Published in Issue Year 2018 Volume: 1 Issue: 1

Cite

APA Fuchs, P. R. (2018). Forcing linearity numbers for coatomic modules. Communications in Advanced Mathematical Sciences, 1(1), 1-4. https://doi.org/10.33434/cams.446020
AMA Fuchs PR. Forcing linearity numbers for coatomic modules. Communications in Advanced Mathematical Sciences. September 2018;1(1):1-4. doi:10.33434/cams.446020
Chicago Fuchs, Peter R. “Forcing Linearity Numbers for Coatomic Modules”. Communications in Advanced Mathematical Sciences 1, no. 1 (September 2018): 1-4. https://doi.org/10.33434/cams.446020.
EndNote Fuchs PR (September 1, 2018) Forcing linearity numbers for coatomic modules. Communications in Advanced Mathematical Sciences 1 1 1–4.
IEEE P. R. Fuchs, “Forcing linearity numbers for coatomic modules”, Communications in Advanced Mathematical Sciences, vol. 1, no. 1, pp. 1–4, 2018, doi: 10.33434/cams.446020.
ISNAD Fuchs, Peter R. “Forcing Linearity Numbers for Coatomic Modules”. Communications in Advanced Mathematical Sciences 1/1 (September 2018), 1-4. https://doi.org/10.33434/cams.446020.
JAMA Fuchs PR. Forcing linearity numbers for coatomic modules. Communications in Advanced Mathematical Sciences. 2018;1:1–4.
MLA Fuchs, Peter R. “Forcing Linearity Numbers for Coatomic Modules”. Communications in Advanced Mathematical Sciences, vol. 1, no. 1, 2018, pp. 1-4, doi:10.33434/cams.446020.
Vancouver Fuchs PR. Forcing linearity numbers for coatomic modules. Communications in Advanced Mathematical Sciences. 2018;1(1):1-4.

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