DIRECT SUMS OF INFINITELY MANY KERNELS

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Atıf İçin Kopyala

Ecevit S., Facchini A., Kosan M. T.

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, cilt.89, sa.2, ss.199-214, 2010 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 89 Sayı: 2
• Basım Tarihi: 2010
• Doi Numarası: 10.1017/s1446788710001539
• Dergi Adı: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.199-214
• Gazi Üniversitesi Adresli: Hayır

Özet

Let kappa be the class of all right R-modules that are kernels of nonzero homomorphisms phi : E-1 -> E-2 for some pair of indecomposable injective right R-modules Et, E2. In a previous paper, we completely characterized when two direct sums A(l) circle plus center dot center dot center dot circle plus A(n) and B-l circle plus center dot center dot center dot circle plus B-m of finitely many modules A(i) and Bi in K are isomorphic. Here we consider the case in which there are arbitrarily, possibly infinitely, many A(i) and B-j in kappa. In both the finite and the infinite case, the behaviour is very similar to that which occurs if we substitute the class kappa with the class u of all uniserial right R-modules (a module is uniserial when its lattice of submodules is linearly ordered).