Yıl 2017, Cilt 22, Sayı 22, Sayfalar 187 - 201 2017-07-11

Block Decomposition For Modules

H. Khabazian [1]

29 64

Block decomposition for rings has been introduced and
shown to be unique in the literature (see [T. Y. Lam, Graduate
Texts in Mathematics, 131, Springer-Verlag, New York, 1991]).
Applying annihilator submodules, we extend this definition to
modules and show that every  module $M$ has a unique block
decomposition $M=\bigoplus_{i=1}^nM_i$ where each $M_i$ is an
annihilator submodule.  We also show that the block decomposition
for any ring $R$ and the
 block decomposition for the module $R_R$, are identical. Block decomposition provides us with a decomposition for $\edmp{M}$ because $\edmp{M}\iso\prod_{i=1}^n\edmp{M_i}$.
 

Annihilator, block orthogonal
  • J. A. Beachy and W. D. Blair, Rings whose faithful left ideals are cofaithful, Pacific J. Math., 58(1) (1975), 1-13.
  • K. R. Goodearl and R. B. Warfield, Jr., An Introduction to Noncommuta- tive Noetherian Rings, Second Edition, London Mathematical Society Student Texts, 61, Cambridge University Press, Cambridge, 2004.
  • H. Khabazian, Existence and uniqueness of a certain type of subdirect product, to appear in Casp. J. Math. Sci.
  • T. Y. Lam, A First Course in Noncommutative Rings, Graduate Texts in Mathematics, 131, Springer-Verlag, New York, 1991.
Konular Matematik ve İstatistik
Dergi Bölümü Makaleler
Yazarlar

Yazar: H. Khabazian
E-posta: khabaz@cc.iut.ac.ir

Bibtex @araştırma makalesi { ieja325944, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2017}, volume = {22}, pages = {187 - 201}, doi = {10.24330/ieja.325944}, title = {Block Decomposition For Modules}, key = {cite}, author = {Khabazian, H.} }
APA Khabazian, H . (2017). Block Decomposition For Modules. International Electronic Journal of Algebra, 22 (22), 187-201. DOI: 10.24330/ieja.325944
MLA Khabazian, H . "Block Decomposition For Modules". International Electronic Journal of Algebra 22 (2017): 187-201 <http://dergipark.gov.tr/ieja/issue/30344/325944>
Chicago Khabazian, H . "Block Decomposition For Modules". International Electronic Journal of Algebra 22 (2017): 187-201
RIS TY - JOUR T1 - Block Decomposition For Modules AU - H. Khabazian Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.325944 DO - 10.24330/ieja.325944 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 187 EP - 201 VL - 22 IS - 22 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.325944 UR - http://dx.doi.org/10.24330/ieja.325944 Y2 - 2018 ER -
EndNote %0 International Electronic Journal of Algebra Block Decomposition For Modules %A H. Khabazian %T Block Decomposition For Modules %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 22 %N 22 %R doi: 10.24330/ieja.325944 %U 10.24330/ieja.325944