Yıl 2014, Cilt 15, Sayı 15, Sayfalar 218 - 248 2014-06-01

CONSTRUCTION OF MODULES WITH A PRESCRIBED DIRECT SUM DECOMPOSITION

Dolors Herbera [1]

177 181

We give some criteria for recognizing local rings that allow us to show that indecomposable AB5∗ modules over commutative rings and couniform modules over noetherian commutative rings have a local endomorphism ring. We also develop some theory on methods to construct modules with a prescribed direct-sum decomposition. As an application we realize an interesting class of commutative monoids as monoids of direct summands of a direct sum of a countable number of copies of a suitable artinian cyclic module, showing that there may appear a rich supply of direct summands that are not a direct sum of artinian modules. An important gadget for proving our realization result is a variation of a method for realizing a given ring as the endomorphism ring of a cyclic (artinian) module due to Armendariz, Fisher and Snider.
AB5∗-module, artinian module, semilocal ring, couniform module, category equivalence, monoid, direct-sum, pullback, pushout
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  • Departament de Matem`atiques
  • Universitat Aut`onoma de Barcelona
  • E-08193 Bellaterra (Barcelona), Spain
  • e-mail: dolors@mat.uab.cat
Konular
Diğer ID JA77TK62SD
Dergi Bölümü Makaleler
Yazarlar

Yazar: Dolors Herbera

Bibtex @ { ieja266249, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2014}, volume = {15}, pages = {218 - 248}, doi = {10.24330/ieja.266249}, title = {CONSTRUCTION OF MODULES WITH A PRESCRIBED DIRECT SUM DECOMPOSITION}, key = {cite}, author = {Herbera, Dolors} }
APA Herbera, D . (2014). CONSTRUCTION OF MODULES WITH A PRESCRIBED DIRECT SUM DECOMPOSITION. International Electronic Journal of Algebra, 15 (15), 218-248. DOI: 10.24330/ieja.266249
MLA Herbera, D . "CONSTRUCTION OF MODULES WITH A PRESCRIBED DIRECT SUM DECOMPOSITION". International Electronic Journal of Algebra 15 (2014): 218-248 <http://dergipark.gov.tr/ieja/issue/25196/266249>
Chicago Herbera, D . "CONSTRUCTION OF MODULES WITH A PRESCRIBED DIRECT SUM DECOMPOSITION". International Electronic Journal of Algebra 15 (2014): 218-248
RIS TY - JOUR T1 - CONSTRUCTION OF MODULES WITH A PRESCRIBED DIRECT SUM DECOMPOSITION AU - Dolors Herbera Y1 - 2014 PY - 2014 N1 - doi: 10.24330/ieja.266249 DO - 10.24330/ieja.266249 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 218 EP - 248 VL - 15 IS - 15 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266249 UR - http://dx.doi.org/10.24330/ieja.266249 Y2 - 2018 ER -
EndNote %0 International Electronic Journal of Algebra CONSTRUCTION OF MODULES WITH A PRESCRIBED DIRECT SUM DECOMPOSITION %A Dolors Herbera %T CONSTRUCTION OF MODULES WITH A PRESCRIBED DIRECT SUM DECOMPOSITION %D 2014 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 15 %N 15 %R doi: 10.24330/ieja.266249 %U 10.24330/ieja.266249
ISNAD Herbera, Dolors . "CONSTRUCTION OF MODULES WITH A PRESCRIBED DIRECT SUM DECOMPOSITION". International Electronic Journal of Algebra 15 / 15 (Haziran 2014): 218-248. http://dx.doi.org/10.24330/ieja.266249