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Communications in Algebra Volume 20, 1992 - Issue 12
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Original Articles

On the prime radical of a module over a commutative ring

James Jenkins Department of Mathematics, University of Glasgow, Glasgow, Scotland, G12 8QW, UK
&
Patrick F. Smith Department of Mathematics, University of Glasgow, Glasgow, Scotland, G12 8QW, UK
Pages 3593-3602 | Received 01 Sep 1991, Published online: 27 Jun 2007

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Babak Amini & Afshin Amini. (2012) On Strongly Superfluous Submodules. Communications in Algebra 40:8, pages 2906-2919.
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DavidE. Rush. (2012) Strongly Prime Submodules, G-Submodules and Jacobson Modules. Communications in Algebra 40:4, pages 1363-1368.
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A. R. Naghipour. (2009) Strongly Prime Submodules. Communications in Algebra 37:7, pages 2193-2199.
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Bülent Saraç. (2009) On Semiprime Submodules. Communications in Algebra 37:7, pages 2485-2495.
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Yücel Tiraş & Mustafa Alkan. (2003) Prime Modules and Submodules. Communications in Algebra 31:11, pages 5253-5261.
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Agustín Marcelo & César Rodríguez. (2000) Radical of submodules and symmetric algebra. Communications in Algebra 28:10, pages 4611-4617.
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Shing Hing Man. (1999) On commutative noetherian rings which satisfy the generalized radical formula. Communications in Algebra 27:8, pages 4075-4088.
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Dilek Pusat-Yilmaz & Patrick F. Smith. (1999) Radicals of submodules of free modules. Communications in Algebra 27:5, pages 2253-2266.
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R. L. McCasland, M. E. Moore & P. F. Smith. (1997) On the spectrum of a module over a commutative ring. Communications in Algebra 25:1, pages 79-103.
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Dilek Pusat-Yilmaz & Patrick F. Smith. (1996) Chain conditions in modules with krull dimension. Communications in Algebra 24:13, pages 4123-4133.
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Wang Fanggui & R. L. McCasland. (1995) Finitely generated reflexive modules over coherent domains. Communications in Algebra 23:8, pages 2897-2911.
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Articles from other publishers (37)

Adam ANEBRI, Hwankoo KIM & Najib MAHDOU. (2023) Baer submodules of modules over commutative rings. International Electronic Journal of Algebra 34:34, pages 31-47.
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MOHAMED KHALIFA. (2022) WHEN PRIME SUBMODULES ARE PRIME IDEALS?. Mathematical Reports 25(75):1, pages 167-177.
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Ortaç ÖNEŞ. (2021) On Prime Ideals Related to an Ideal in a Commutative Ring. Gazi University Journal of Science Part A: Engineering and Innovation 8:4, pages 451-458.
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Morteza NOFERESTİ, Hosein FAZAELİ MOGHİMİ & Mohammad Hossein HOSSEİNİ. (2021) Mappings between the lattices of saturated submodules with respect to a prime ideal. Hacettepe Journal of Mathematics and Statistics 50:1, pages 243-254.
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Annet Kyomuhangi & David Ssevviiri. (2020) The locally nilradical for modules over commutative rings. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 61:4, pages 759-769.
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Ashkan NİKSERESHT. (2020) Delta operation on modules, prime and radical submodules and primary decomposition. Hacettepe Journal of Mathematics and Statistics 49:4, pages 1303-1314.
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Le Phuong Thao. (2018) Almost prime submodules. Asian-European Journal of Mathematics 13:01, pages 2050019.
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O. Öneş & M. Alkan. (2020) The Radical Formula for Noncommutative Rings. Ukrainian Mathematical Journal 71:9, pages 1419-1428.
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Sang Cheol Lee & Rezvan Varmazyar. (2019) Semiprime submodules of a module and related concepts. Journal of Algebra and Its Applications 18:08, pages 1950147.
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Agustín Marcelo, Félix Marcelo & César Rodríguez. 2016. Geometry, Algebra and Applications: From Mechanics to Cryptography. Geometry, Algebra and Applications: From Mechanics to Cryptography 147 156 .
Anand Parkash. (2014) One dimensional local domains and radical formula. Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 56:2, pages 729-733.
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N. Dehghani & M. R. Vedadi. (2015) A characterization of modules embedding in products of primes and enveloping condition for their class. Journal of Algebra and Its Applications 14:04, pages 1550051.
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John A. Beachy, Mahmood Behboodi & Faezeh Yazdi. (2013) PRIME M-IDEALS, M-PRIME SUBMODULES, M-PRIME RADICAL AND M-BAER'S LOWER NILRADICAL OF MODULES. Journal of the Korean Mathematical Society 50:6, pages 1271-1290.
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Anand Parkash. (2012) Arithmetical rings satisfy the radical formula. Journal of Commutative Algebra 4:2.
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Hwan-Koo Kim. (2012) MODULE-THEORETIC CHARACTERIZATIONS OF KRULL DOMAINS. Bulletin of the Korean Mathematical Society 49:3, pages 601-608.
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A. A. Estaji & S. Tajnia. (2011) Prime subacts over commutative monoids with zero. Lobachevskii Journal of Mathematics 32:4, pages 358-365.
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DAVID E. RUSH. (2011) NOETHERIAN SPECTRUM ON RINGS AND MODULES. Glasgow Mathematical Journal 53:3, pages 707-715.
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Nguyen Van Sanh, S. Asawasamrit, K. F. U. Ahmed & Le Phuong Thao. (2012) ON PRIME AND SEMIPRIME GOLDIE MODULES. Asian-European Journal of Mathematics 04:02, pages 321-334.
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M. BAZIAR & M. BEHBOODI. (2011) CLASSICAL PRIMARY SUBMODULES AND DECOMPOSITION THEORY OF MODULES. Journal of Algebra and Its Applications 08:03, pages 351-362.
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A. AZIZI. (2009) RADICAL FORMULA AND WEAKLY PRIME SUBMODULES. Glasgow Mathematical Journal 51:2, pages 405-412.
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M. Behboodi. (2008) On the prime radical and Baer’s lower nilradical of modules. Acta Mathematica Hungarica 122:3, pages 293-306.
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H. Koohy. (2007) On finiteness of multiplication modules. Acta Mathematica Hungarica 118:1-2, pages 1-7.
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Mustafa Alkan & Yücel Tiraş. (2007) On Prime Submodules. Rocky Mountain Journal of Mathematics 37:3.
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MAHMOOD BEHBOODI. (2011) A GENERALIZATION OF BAER'S LOWER NILRADICAL FOR MODULES. Journal of Algebra and Its Applications 06:02, pages 337-353.
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DILEK BUYRUK & DILEK PUSAT-YILMAZ. (2007) MODULES OVER PRÜFER DOMAINS WHICH SATISFY THE RADICAL FORMULA. Glasgow Mathematical Journal 49:1, pages 127-131.
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A. Azizi. (2007) Radical formula and prime submodules. Journal of Algebra 307:1, pages 454-460.
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MIGUEL FERRERO & VIRGINIA RODRIGUES. (2011) ON PRIME AND SEMIPRIME MODULES AND COMODULES. Journal of Algebra and Its Applications 05:05, pages 681-694.
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Mustafa Alkan & Yücel Tiraş. (2006) Projective modules and prime submodules. Czechoslovak Mathematical Journal 56:2, pages 601-611.
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CHRISTIAN LOMP. (2011) PRIME ELEMENTS IN PARTIALLY ORDERED GROUPOIDS APPLIED TO MODULES AND HOPF ALGEBRA ACTIONS. Journal of Algebra and Its Applications 04:01, pages 77-97.
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Shing Hing Man & Patrick F. Smith. (2002) On chains of prime submodules. Israel Journal of Mathematics 127:1, pages 131-155.
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Yücel Tiras & Abdullah Harmanci. (2000) On prime submodules and primary decomposition. Czechoslovak Mathematical Journal 50:1, pages 83-90.
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Yücel Tıraş, Abdullah Harmancı & P.F. Smith. (1999) A Characterization of Prime Submodules. Journal of Algebra 212:2, pages 743-752.
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Agustín Marcelo, Félix Marcelo & César Rodríguez. 1999. Computer Algebra in Scientific Computing CASC’99. Computer Algebra in Scientific Computing CASC’99 287 292 .
R.L. McCasland, M.E. Moore & P.F. Smith. (1998) An Introduction to Zariski Spaces over Zariski Topologies. Rocky Mountain Journal of Mathematics 28:4.
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Ka Hin Leung & Shing Hing Man. (2009) On commutative Noetherian rings which satisfy the radical formula. Glasgow Mathematical Journal 39:3, pages 285-293.
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Shing Hing Man. (1996) One dimensional domains which satisfy the radical formula are Dedekind domains. Archiv der Mathematik 66:4, pages 276-279.
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H. Sharif, Y. Sharifi & S. Namazi. (1996) Rings satisfying the radical formula. Acta Mathematica Hungarica 71:1-2, pages 103-108.
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