Article
| Title: | Some homological properties of amalgamated modules along an ideal (English) |
| Author: | Shoar, Hanieh |
| Author: | Salimi, Maryam |
| Author: | Tehranian, Abolfazl |
| Author: | Rasouli, Hamid |
| Author: | Tavasoli, Elham |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 2 |
| Year: | 2023 |
| Pages: | 475-486 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $R$ and $S$ be commutative rings with identity, $J$ be an ideal of $S$, $f \colon R \to S$ be a ring homomorphism, $M$ be an $R$-module, $N$ be an $S$-module, and let $\varphi \colon M \to N$ be an $R$-homomorphism. The amalgamation of $R$ with $S$ along $J$ with respect to $f$ denoted by $R \bowtie ^{f} J$ was introduced by M. D'Anna et al. (2010). Recently, R. El Khalfaoui et al. (2021) introduced a special kind of $(R \bowtie ^{f} J)$-module called the amalgamation of $M$ and $N$ along $J$ with respect to $\varphi $, and denoted by $M \bowtie ^{\varphi } JN$. We study some homological properties of the $(R \bowtie ^{f} J)$-module $M \bowtie ^{\varphi } JN$. Among other results, we investigate projectivity, flatness, injectivity, Cohen-Macaulayness, and prime property of the $(R \bowtie ^{f} J)$-module $M \bowtie ^{\varphi } JN$ in connection to their corresponding properties of the $R$-modules $M$ and $JN$. (English) |
| Keyword: | amalgamation of ring |
| Keyword: | amalgamation of module |
| Keyword: | Cohen-Macaulay |
| Keyword: | injective module |
| Keyword: | projective(flat) module |
| MSC: | 13A15 |
| MSC: | 13C10 |
| MSC: | 13C11 |
| MSC: | 13C14 |
| MSC: | 13C15 |
| idZBL: | Zbl 07729518 |
| idMR: | MR4586905 |
| DOI: | 10.21136/CMJ.2023.0411-21 |
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| Date available: | 2023-05-04T17:46:09Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151668 |
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| Reference: | [1] Bouba, E. M., Mahdou, N., Tamekkante, M.: Duplication of a module along an ideal.Acta Math. Hung. 154 (2018), 29-42. Zbl 1399.13011, MR 3746520, 10.1007/s10474-017-0775-6 |
| Reference: | [2] Brodmann, M. P., Sharp, R. Y.: Local Cohomology: An Algebraic Introduction with Geometric Applications.Cambridge Studies in Advanced Mathematics 60. Cambridge University Press, Cambridge (1998). Zbl 0903.13006, MR 1613627, 10.1017/CBO9780511629204 |
| Reference: | [3] D'Anna, M.: A construction of Gorenstein rings.J. Algebra 306 (2006), 507-519. Zbl 1120.13022, MR 2271349, 10.1016/j.jalgebra.2005.12.023 |
| Reference: | [4] D'Anna, M., Finocchiaro, C. A., Fontana, M.: Amalgamated algebras along an ideal.Commutative Algebra and Its Applications Walter de Gruyter, Berlin (2009), 155-172. Zbl 1177.13043, MR 2606283, 10.1515/9783110213188.155 |
| Reference: | [5] D'Anna, M., Finocchiaro, C. A., Fontana, M.: Properties of chains of prime ideals in an amalgamated algebra along an ideal.J. Pure Appl. Algebra 214 (2010), 1633-1641. Zbl 1191.13006, MR 2593689, 10.1016/j.jpaa.2009.12.008 |
| Reference: | [6] D'Anna, M., Fontana, M.: An amalgamated duplication of a ring along an ideal: The basic properties.J. Algebra Appl. 6 (2007), 443-459. Zbl 1126.13002, MR 2337762, 10.1142/S0219498807002326 |
| Reference: | [7] D'Anna, M., Fontana, M.: The amalgamated duplication of a ring along a multiplicative-cannonical ideal.Ark. Mat. 45 (2007), 241-252. Zbl 1143.13002, MR 2342602, 10.1007/s11512-006-0038-1 |
| Reference: | [8] Khalfaoui, R. El, Mahdou, N., Sahandi, P., Shirmohammadi, N.: Amalgamated modules along an ideal.Commun. Korean Math. Soc. 36 (2021), 1-10. Zbl 1467.13026, MR 4215837, 10.4134/CKMS.c200064 |
| Reference: | [9] Enochs, E.: Flat covers and flat cotorsion modules.Proc. Am. Math. Soc. 92 (1984), 179-184. Zbl 0522.13008, MR 0754698, 10.1090/S0002-9939-1984-0754698-X |
| Reference: | [10] Kosmatov, N. V.: Bounds for the homological dimensions of pullbacks.J. Math. Sci., New York 112 (2002), 4367-4370. Zbl 1052.16006, MR 1757826, 10.1023/A:1020351104689 |
| Reference: | [11] Salimi, M., Tavasoli, E., Yassemi, S.: The amalgamated duplication of a ring along a semidualizing ideal.Rend. Semin. Mat. Univ. Padova 129 (2013), 115-127. Zbl 1279.13025, MR 3090634, 10.4171/RSMUP/129-8 |
| Reference: | [12] Shapiro, J.: On a construction of Gorenstein rings proposed by M. D'Anna.J. Algebra 323 (2010), 1155-1158. Zbl 1184.13069, MR 2578598, 10.1016/j.jalgebra.2009.12.003 |
| Reference: | [13] Tavasoli, E.: Some homological properties of amalgamation.Mat. Vesn. 68 (2016), 254-258. Zbl 1458.13026, MR 3554642 |
| Reference: | [14] Tiraş, Y., Tercan, A., Harmanci, A.: Prime modules.Honam Math. J. 18 (1996), 5-15. Zbl 0948.13004, MR 1402357 |
| Reference: | [15] Xu, J.: Flat Covers of Modules.Lecture Notes in Mathematics 1634. Springer, Berlin (1996). Zbl 0860.16002, MR 1438789, 10.1007/BFb0094173 |
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