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Original Articles

Depth and Stanley Depth of Multigraded Modules

Pages 773-784 | Received 11 Dec 2008, Published online: 18 Feb 2010

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (6)

Bakhtawar Shaukat, Ahtsham Ul Haq & Muhammad Ishaq. (2023) Some algebraic Invariants of the residue class rings of the edge ideals of perfect semiregular trees. Communications in Algebra 51:6, pages 2364-2383.
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Zahid Iqbal, Muhammad Ishaq & Muhammad Aamir. (2018) Depth and Stanley depth of the edge ideals of square paths and square cycles. Communications in Algebra 46:3, pages 1188-1198.
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Mircea Cimpoeaş. (2018) A class of square-free monomial ideals associated to two integer sequences. Communications in Algebra 46:3, pages 1179-1187.
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Dorin Popescu. (2013) The Stanley Conjecture on Intersections of Four Monomial Prime Ideals. Communications in Algebra 41:11, pages 4351-4362.
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Muhammad Ishaq & Muhammad Imran Qureshi. (2013) Upper and Lower Bounds for the Stanley Depth of Certain Classes of Monomial Ideals and Their Residue Class Rings. Communications in Algebra 41:3, pages 1107-1116.
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Muhammad Ishaq. (2012) Upper Bounds for the Stanley Depth. Communications in Algebra 40:1, pages 87-97.
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Articles from other publishers (33)

Bakhtawar Shaukat, Muhammad Ishaq & Ahtsham Ul Haq. (2024) Algebraic invariants of edge ideals of some circulant graphs. AIMS Mathematics 9:1, pages 868-895.
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Kamalesh Saha. (2023) The v-Number and Castelnuovo-Mumford Regularity of Cover Ideals of Graphs. International Mathematics Research Notices.
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Ying Wang, Sidra Sharif, Muhammad Ishaq, Fairouz Tchier, Ferdous M. Tawfiq & Adnan Aslam. (2023) Depth and Stanley Depth of the Edge Ideals of r-Fold Bristled Graphs of Some Graphs. Mathematics 11:22, pages 4646.
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Raheleh Jafari & Ali Akbar Yazdan Pour. (2023) SHEDDING VERTICES AND ASS-DECOMPOSABLE MONOMIAL IDEALS. Rocky Mountain Journal of Mathematics 53:1.
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Tazeen Ayesha & Muhammad Ishaq. (2023) Some algebraic invariants of the edge ideals of perfect $ [h, d] $-ary trees and some unicyclic graphs. AIMS Mathematics 8:5, pages 10947-10977.
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Guiling Zeng, Muhammad Mobeen Munir, Raheel Farooki, Muhammad Athar & Jia Bao Liu. (2022) Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis. Journal of Mathematics 2022, pages 1-8.
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K. Kimura, M. R. Pournaki, S. A. Seyed Fakhari, N. Terai & S. Yassemi. (2022) A glimpse to most of the old and new results on very well-covered graphs from the viewpoint of commutative algebra. Research in the Mathematical Sciences 9:2.
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Malik Muhammad Suleman Shahid, Muhammad Ishaq, Anuwat Jirawattanapanit & Khanyaluck Subkrajang. (2022) Depth and Stanley depth of the edge ideals of multi triangular snake and multi triangular ouroboros snake graphs. AIMS Mathematics 7:9, pages 16449-16463.
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Zahid IQBAL, Muhammad ISHAQ & Muhammad Ahsan BİNYAMİN. (2021) Depth and Stanley depth of the edge ideals of the strong product of some graphs. Hacettepe Journal of Mathematics and Statistics 50:1, pages 92-109.
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Naeem Ud Din, Muhammad Ishaq & Zunaira Sajid. (2021) Values and bounds for depth and Stanley depth of some classes of edge ideals. AIMS Mathematics 6:8, pages 8544-8566.
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Zahid IqbalMuhammad Ishaq. (2019) Depth and Stanley depth of the edge ideals of the powers of paths and cycles. Analele Universitatii "Ovidius" Constanta - Seria Matematica 27:3, pages 113-135.
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Jia-Bao Liu, Mobeen Munir, Raheel Farooki, Muhammad Imran Qureshi & Quratulien Muneer. (2019) Stanley Depth of Edge Ideals of Some Wheel-Related Graphs. Mathematics 7:2, pages 202.
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Giulio Caviglia, Huy Tài Hà, Jürgen Herzog, Manoj Kummini, Naoki Terai & Ngo Viet Trung. (2018) Depth and regularity modulo a principal ideal. Journal of Algebraic Combinatorics 49:1, pages 1-20.
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Zahid Iqbal & Muhammad Ishaq. (2019) Depth and Stanley depth of edge ideals associated to some line graphs. AIMS Mathematics 4:3, pages 686-698.
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Giuseppe Favacchio, Elena Guardo & Juan Migliore. (2018) On the arithmetically Cohen-Macaulay property for sets of points in multiprojective spaces. Proceedings of the American Mathematical Society 146:7, pages 2811-2825.
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KYOUKO KIMURA, NAOKI TERAI & SIAMAK YASSEMI. (2017) THE PROJECTIVE DIMENSION OF THE EDGE IDEAL OF A VERY WELL-COVERED GRAPH. Nagoya Mathematical Journal 230, pages 160-179.
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Mircea Cimpoeas. (2018) On the Stanley Depth of Powers of Some Classes of Monomial Ideals. Bulletin of the Iranian Mathematical Society 44:3, pages 739-747.
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S.A. Seyed Fakhari. (2017) On the Stanley depth of powers of edge ideals. Journal of Algebra 489, pages 463-474.
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Lizhong Chu & V. H. Jorge Pérez. (2016) The Stanley regularity of complete intersections and ideals of mixed products. Journal of Algebra and Its Applications 16:07, pages 1750122.
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Lukas Katthän. (2016) Betti Posets and the Stanley Depth. Arnold Mathematical Journal 2:2, pages 267-276.
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Daniel Campos, Ryan Gunderson, Susan Morey, Chelsey Paulsen & Thomas Polstra. (2016) Depths and Stanley depths of path ideals of spines. Involve, a Journal of Mathematics 9:1, pages 155-170.
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Louiza Fouli & Susan Morey. (2015) A lower bound for depths of powers of edge ideals. Journal of Algebraic Combinatorics 42:3, pages 829-848.
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Gaetana Restuccia, Zhongming Tang & Rosanna Utano. (2015) Stanley conjecture on monomial ideals of mixed products. Journal of Commutative Algebra 7:1.
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Yi-Huang Shen. (2014) Stanley depth of weakly 0-decomposable ideals. Archiv der Mathematik 104:1, pages 3-9.
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S. A. Seyed Fakhari. (2014) Stanley depth of weakly polymatroidal ideals. Archiv der Mathematik 103:3, pages 229-233.
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Adrian Popescu & Dorin Popescu. 2014. Bridging Algebra, Geometry, and Topology. Bridging Algebra, Geometry, and Topology 231 248 .
M. Pournaki, S. A. Seyed Fakhari & S. Yassemi. (2013) Stanley depth of powers of the edge ideal of a forest. Proceedings of the American Mathematical Society 141:10, pages 3327-3336.
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Jürgen Herzog. 2013. Monomial Ideals, Computations and Applications. Monomial Ideals, Computations and Applications 3 45 .
Jürgen Herzog, Dorin Popescu & Marius Vladoiu. (2011) Stanley depth and size of a monomial ideal. Proceedings of the American Mathematical Society 140:2, pages 493-504.
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Azeem Haider & Sardar Khan. (2011) Stanley’s conjecture for critical ideals. Studia Scientiarum Mathematicarum Hungarica 48:2, pages 220-226.
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Sumiya Nasir & Asia Rauf. (2010) Stanley decompositions in localized polynomial rings. Manuscripta Mathematica 135:1-2, pages 151-164.
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Winfried Bruns, Christian Krattenthaler & Jan Uliczka. (2010) Stanley decompositions and Hilbert depth in the Koszul complex. Journal of Commutative Algebra 2:3.
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Mircea Cimpoeaş. (2009) Stanley depth of monomial ideals with small number of generators. Open Mathematics 7:4.
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