| Title:
|
Comultiplication modules over a pullback of Dedekind domains (English) |
| Author:
|
Atani, Reza Ebrahimi |
| Author:
|
Atani, Shahabaddin Ebrahimi |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
1103-1114 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
First, we give complete description of the comultiplication modules over a Dedekind domain. Second, if $R$ is the pullback of two local Dedekind domains, then we classify all indecomposable comultiplication $R$-modules and establish a connection between the comultiplication modules and the pure-injective modules over such domains. (English) |
| Keyword:
|
pullback |
| Keyword:
|
separated modules and representations |
| Keyword:
|
non-separated modules |
| Keyword:
|
comultiplication modules |
| Keyword:
|
dedekind domain |
| Keyword:
|
pure-injective modules |
| Keyword:
|
Prüfer modules |
| MSC:
|
13C05 |
| MSC:
|
13C13 |
| MSC:
|
16D70 |
| idZBL:
|
Zbl 1224.13012 |
| idMR:
|
MR2563581 |
| . |
| Date available:
|
2010-07-20T16:05:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140540 |
| . |
| Reference:
|
[1] Assen, I., Simson, D., Skowroński, A.: Representation Theory of Associative Algebra. Vol. 1.Techniques of Representation Theory. London Math. Soc. Student Texts 65, Cambridge Univ. Press, Cambridge-New York (2007). MR 2197389 |
| Reference:
|
[2] Ansari-Toroghy, H., Farshadifar, F.: On endomorphisms of multiplication and comultiplication modules.Archivum Mathematicum 44 (2008), 9-15. MR 2431226 |
| Reference:
|
[3] Bass, H.: On the ubiquity of Gorenstein rings.Math. Z. 82 (1963), 8-29. Zbl 0112.26604, MR 0153708, 10.1007/BF01112819 |
| Reference:
|
[4] El-Bast, Z. A., Smith, P. F.: Multiplication modules.Comm. Algebra. 16 (1988), 755-779. Zbl 0642.13003, MR 0932633, 10.1080/00927878808823601 |
| Reference:
|
[5] Atani, S. Ebrahimi: On pure-injective modules over pullback rings.Comm. Algebra 28 (2000), 4037-4069. MR 1772008, 10.1080/00927870008827074 |
| Reference:
|
[6] Atani, S. Ebrahimi: On secondary modules over pullback rings.Comm. Algebra 30 (2002), 2675-2685. Zbl 1011.13004, MR 1908232, 10.1081/AGB-120003982 |
| Reference:
|
[7] Atani, S. Ebrahimi: On prime modules over pullback rings.Czech. Math. J. 54 (2004), 781-789. MR 2086734, 10.1007/s10587-004-6426-4 |
| Reference:
|
[8] Atani, S. Ebrahimi, Farzalipour, F.: Weak multiplication modules over a pullback of Dedekind domains.(to appear) in Colloq. Math. MR 2457281 |
| Reference:
|
[9] Atani, S. Ebrahimi: Indecomposable weak multiplication modules over Dedekind domains.Demonstratio Mathematica XLI 41 (2008), 33-43. MR 2394295 |
| Reference:
|
[10] Atani, S. Ebrahimi: On secondary modules over Dedekind domains.Southeast Asian Bull. Math. 25 (2001), 1-6. MR 1832737, 10.1007/s10012-001-0001-9 |
| Reference:
|
[11] Facchini, A., Vamos, P.: Injective modules over pullbacks.J. London Math. Soc. 31 (1985), 125-138. Zbl 0526.16014, MR 0812770 |
| Reference:
|
[12] Kietpiński, R.: On $\Gamma$-pure injective modules.Bull. Polon. Acad. Sci. Math. 15 (1967), 127-131. |
| Reference:
|
[13] Levy, L.: Modules over pullbacks and subdirect sums.J. Algebra 71 (1981), 50-61. Zbl 0508.16008, MR 0627425, 10.1016/0021-8693(81)90106-X |
| Reference:
|
[14] Levy, L.: Modules over Dedekind-like rings.J. Algebra 93 (1985), 1-116. Zbl 0564.13010, MR 0780485, 10.1016/0021-8693(85)90176-0 |
| Reference:
|
[15] Levy, L.: Mixed modules over $ZG$, $G$ cyclic of prime order, and over related Dedekind pullbacks.J. Algebra 70 (1981), 62-114. Zbl 0508.16009, MR 0627426, 10.1016/0021-8693(81)90107-1 |
| Reference:
|
[16] Nazarova, L. A., Roiter, A. V.: Finitely generated modules over a dyad of local Dedekind rings and finite group having an abelian normal subgroup of index $p$.Russian Izv. Acad. Nauk. SSSR 33 (1969), 65-89. MR 0260859 |
| Reference:
|
[17] Prest, M.: Model Theory and Modules.London Mathematical Society, Cambridge University Press, Cambridge (1988). Zbl 0634.03025, MR 0933092 |
| Reference:
|
[18] Prest, M.: Ziegler spectra of tame hereditary algebras.J. Algebra 207 (1998), 146-164. Zbl 0936.16014, MR 1643078, 10.1006/jabr.1998.7472 |
| Reference:
|
[19] Simson, D.: Linear Representations of Partially Ordered Sets and Vector Space Categories.Algebra, Logic and Applications. Vol. 4, Gordon and Breach Science Publishers, Switzerland-Australia (1992). Zbl 0818.16009, MR 1241646 |
| Reference:
|
[20] Simson, D.: On Corner type Endo-Wild algebras.J. Pure Appl. Algebra 202 (2005), 118-132. Zbl 1151.16014, MR 2163404, 10.1016/j.jpaa.2005.01.012 |
| Reference:
|
[21] Sharp, R. Y.: Steps in Commutative Algebra.London Mathematical Society, Student Texts, Vol. 19, Cambridge University Press, Cambridge (1990). Zbl 0703.13001, MR 1070568 |
| Reference:
|
[22] Warfield, R. B.: Purity and algebraic compactness for modules.Pacific J. Math. 28 (1969), 699-719. Zbl 0172.04801, MR 0242885, 10.2140/pjm.1969.28.699 |
| Reference:
|
[23] Wiseman, A. N.: Projective modules over pullback rings.Math. Proc. Cambridge Philos. Soc. 97 (1985), 399-106. Zbl 0588.16016, MR 0778673, 10.1017/S0305004100062964 |
| . |
