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Forcing linearity numbers for coatomic modules

Yıl 2018, , 1 - 4, 30.09.2018

Peter R. Fuchs

https://doi.org/10.33434/cams.446020

Öz

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 $n\in \left\{ 0,1,2,\infty \right\} \cup \left\{ q+2\left\vert q\text{ is a prime power}\right. \right\} .$

Anahtar Kelimeler

Homogeneous functions Forcing linearity numbers Coatomic modules

Kaynakça

  • [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.

Yıl 2018, , 1 - 4, 30.09.2018

Peter R. Fuchs

https://doi.org/10.33434/cams.446020

Öz

Kaynakça

  • [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.
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Peter R. Fuchs 0000-0001-9165-3688

Yayımlanma Tarihi 30 Eylül 2018
Gönderilme Tarihi 19 Temmuz 2018
Kabul Tarihi 19 Eylül 2018
Yayımlandığı Sayı Yıl 2018

Kaynak Göster

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. Eylül 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, sy. 1 (Eylül 2018): 1-4. https://doi.org/10.33434/cams.446020.
EndNote Fuchs PR (01 Eylül 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, c. 1, sy. 1, ss. 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 (Eylül 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, c. 1, sy. 1, 2018, ss. 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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