Yıl 2017, Cilt 21, Sayı 21, Sayfalar 103 - 120 2017-01-17
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## FINITE LATTICES OF PRERADICALS AND FINITE REPRESENTATION TYPE RINGS

#### Rogelio Fernandez-Alonso [1] , Dolors Herbera [2]

##### 199 168

In this paper we study some classes of rings which have a finite lattice of preradicals. We characterize commutative rings with this condition as finite representation type rings, i.e., artinian principal ideal rings. In general, it is easy to see that the lattice of preradicals of a left pure semisimple ring is a set, but it may be infinite. In fact, for a finite dimensional path algebra Λ over an algebraically closed field we prove that Λ-pr is finite if and only if its quiver is a disjoint union of finite quivers of type An; hence there are path algebras of finite representation type such that its lattice of preradicals is an infinite set. As an example, we describe the lattice of preradicals over Λ = kQ when Q is of type An and it has the canonical orientation

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Konular Makaleler Yazar: Rogelio Fernandez-Alonso Yazar: Dolors Herbera
 Bibtex @araştırma makalesi { ieja296155, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2017}, volume = {21}, pages = {103 - 120}, doi = {10.24330/ieja.296155}, title = {FINITE LATTICES OF PRERADICALS AND FINITE REPRESENTATION TYPE RINGS}, key = {cite}, author = {Fernandez-Alonso, Rogelio and Herbera, Dolors} } APA Fernandez-Alonso, R , Herbera, D . (2017). FINITE LATTICES OF PRERADICALS AND FINITE REPRESENTATION TYPE RINGS. International Electronic Journal of Algebra, 21 (21), 103-120. DOI: 10.24330/ieja.296155 MLA Fernandez-Alonso, R , Herbera, D . "FINITE LATTICES OF PRERADICALS AND FINITE REPRESENTATION TYPE RINGS". International Electronic Journal of Algebra 21 (2017): 103-120 Chicago Fernandez-Alonso, R , Herbera, D . "FINITE LATTICES OF PRERADICALS AND FINITE REPRESENTATION TYPE RINGS". International Electronic Journal of Algebra 21 (2017): 103-120 RIS TY - JOUR T1 - FINITE LATTICES OF PRERADICALS AND FINITE REPRESENTATION TYPE RINGS AU - Rogelio Fernandez-Alonso , Dolors Herbera Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.296155 DO - 10.24330/ieja.296155 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 103 EP - 120 VL - 21 IS - 21 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.296155 UR - http://dx.doi.org/10.24330/ieja.296155 Y2 - 2016 ER - EndNote %0 International Electronic Journal of Algebra FINITE LATTICES OF PRERADICALS AND FINITE REPRESENTATION TYPE RINGS %A Rogelio Fernandez-Alonso , Dolors Herbera %T FINITE LATTICES OF PRERADICALS AND FINITE REPRESENTATION TYPE RINGS %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 21 %N 21 %R doi: 10.24330/ieja.296155 %U 10.24330/ieja.296155 ISNAD Fernandez-Alonso, Rogelio , Herbera, Dolors . "FINITE LATTICES OF PRERADICALS AND FINITE REPRESENTATION TYPE RINGS". International Electronic Journal of Algebra 21 / 21 (Ocak 2017): 103-120. http://dx.doi.org/10.24330/ieja.296155