**Associate Professor**

Mathematics

**Email:**

**Office:**

**Joined ADA:**

ralizada[at]ada.edu.az

B214

2023

- Abstract Algebra
- Group Theory
- Combinatorial Analysis
- Linear Algebra
- Abelian Groups

- PhD, Lomonosov Moscow State University
- BS/MS, Lomonosov Moscow State University

- https://www.researchgate.net/profile/Rafail-Alizade
- On global dimensions of inductively closed proper classes in the category of abelian groups. Izvestiya Akademii Nauk Azerb. SSR, ser. fiz.-tech. math. nauk, 2(1983), pp. 9-14.
- On heredity of coprojective and coinjective properties for some proper classes. Izvestiya Akademii Nauk Azerb. SSR, ser. fiz.-tech. math. nauk, 5(1983), pp.. 3-7.
- Cotorsion groups and functor lim-1. Izvestiya Akademii Nauk Azerb. SSR, ser. fiz. - tech. math. nauk, 6(1983), pp. 3-4.
- On the global dimension of some proper classes. Uspechi. matem. nauk, 40:1(1985), pp. 181-182.
- On Kepka's proper classes. Math. Notes, 37:2(1985), pp. 268-273.
- On the proper classes of short exact sequences in the category of abelian groups. Math. Notes, 40:1(1986), pp. 3-15.
- On Topology Induced by Bohr Compactification Indian Journal of Pure and Appl.Math. 30:11(1999) (Coauthor: A.Pancar)
- Modules Whose Maximal Submodules Have Supplements Communications in Algebra, 29:6 (2001), 2389-2405 (Coauthors: G.Bilhan, P.Smith)
- Special Precovers in Cotorsion Theories, Proceedings of Edinburgh Math. Society, 45(2002)pp.411-420 (Coauthor: K. Akıncı)
- Cofinitely weak supplemented modules Communications in Algebra, 31:11 (2003), 5377-5390 (Coauthor: E. Büyükaşık)
- Extensions of weakly supplemented modules Math. Scand. v. 103 ( 2008), 1 – 8 (Coauthor: E.Büyükaşık).
- Cofinitely weak supplemented lattices Indian J. pure appl. Math. 40:5(2009), 1 - 9 (Coauthor: E.Toksoy).
- Resolutions in cotorsion theories International Conference on Mathematical Science, 23-27 November 2010 , Bolu Turkey, AIP Conference Psoceedings 1309, pp.761-768 (Coauthor: K.Akıncı).
- Cofinitely supplemented modular lattices. Arabian Journal for Science and Engineering, 36:6(2011), pp. 919-923 (Coauthor: E.Toksoy).
- The Proper Class Generated by Weak Supplements Communications in Algebra 42(1) (2014), pp. 56-72 (Coauthors: Y.Demirci, Y. Durgun, D. Pusat-Yılmaz).
- Rings and modules characterized by opposites of injectivity Journal of Algebra 409 (2014), pp. 182 – 198 (Coauthors: E.Büyükaşık, N.Er).
- Small supplements, weak supplements and proper classes Hacettepe Journal of Mathematics and Statistics 45:3 (2016), 649-661 (Coauthors: E.Büyükaşık, Y. Durgun) Doi: 10.15672/HJMS.20164512507
- Abelian Groups whose nonzero endomorphisms have nonessential kernels Journal of Algebra and Its Applications 16:1(2016),1750048 Coauthor: Surajo Ibrahim Isah)
- Closures of Proper Classes Miskolc Mathematical Notes) 17:2(2016), pp.723-738 (Coauthor: Y.Demirci) DOI: 10.18514/MMN.2016.1566
- Poor and pi-poor abelian groups Communications in Algebra 45(1)(2017), pp.420-427 (Coauthor: E.Büyükaşık) Doi: 10.1080/00927872.2016.1175585.
- Test Modules for flatness Rendiconti Del Seminario Matematico Della Universita Di Padova 137(2017), pp. 75-91 (Coauthor: Y. Durgun)
- Modules and abelian groups with minimal (pure-) projectivity domains Journal of Algebra and Its Applications 16:2 (2017) (Coauthor: D.D. Sipahi)
- Co-coatomically supplemented modules Ukrainian Mathematical Journal 69:7 (2017), pp.1007-1018 (Coauthor: S. Güngör).
- Co-coatomically supplemented and co-coatomically semiperfect modules Hacettepe Journal of Mathematics and Statistics, 47:6(2018),1417-1426(Coauthor: S.Güngör) Doi: 10.15672/HJMS.20154413844
- Poor modules with no proper poor direct summands, Journal of Algebra, 502(2018), 24-44 (Coauthors: E. Büyükaşık, S. R.Lopez-Permouth, L. Yang)
- On Rings with One Middle Class of Injectivity Domains. Mathematical Commu-nications 27(2022), 109-126 (Coauthors, Y.M.Demirci, B.N. Türkmen, E.Türkmen).
- Pure Direct Projective Modules, Journal of Algebra and Its Applications (Coauthor: S.E.Toksoy).
- Modules and abelian groups with restricted domain of projectivity (submitted) (Coauthor: D.D. Sipahi).
- Rectractable and Coretractable Abelian Groups (submitted) (Coauthor: E.Büyükaşık)
- On Purities Relative to Minimal Right Ide-als (to appear in Lobachevsky Journal of Math-ematics) (Coauthors: Y.Alagöz, E.Büyükaşık and S. Sağbaş).
- Yusuf Alagöz, Rafail Alizade, Engin Buyükaşık and Selcuk Sağbaş, On Purities Relative to Minimal Right Ideals Lobachevskii Journal of Mathematics, 2023, Vol. 44, No. 7, pp. 2553–2562.
- Rafail Alizade, Damla Dede Sipahi Modules and abelian groups with restricted domain of projectivity Journal of Algebra and Its Applications (2025) 2550173
- On closures of proper classes. Proc. Baku Int. Topol. Conf., Baku, 1989, pp. 12-19.
- Resolutions in cotorsion theories International Conference on Mathematical Science, 23-27 November 2010 , Bolu Turkey, AIP Conference Psoceedings 1309, pp.761-768. (Coauthor: Karen Akıncı).
- On the global dimension of proper classes in the category of abelian groups. IX. All-Union symposium on group theory. Abstracts, Moscow, 1984, p. 171.
- On embedding G ®G*. V. Tiraspol Sym-posium on the General Topology and its Applications. Abstracts, Kishinev, 1985, p. 6.
- On Hart's proper classes. XVIII. All-Union Algebraic Conference, Abstracts, Kishinev,1985.
- On proper classes including Text. Baku International topological Conference, Abstracts, part 1, Baku, 1987, p. 8.
- Global dimension and some operations on proper classes. XIX. All-Union Algebraic Conference. Abstracts, Lvov, 1987.
- On operations over proper classes of short exact sequences International Conf. Dedicated 90th Ann. of Pontryagin, Moscow 1998, p.10-11 (Coauthors:G.Bilhan,A.Pancar)
- Cotorsion Theories and Resolutions International Congress of Mathematicians. Abstracts of Short Communications and Poster Sessions. Beijing, 2002, August 20-28, p.9. (Coauthor: K. Akıncı).
- Cofinitely Weak Supplemented Lattices International Conference on Modules and Comodules Dedicated to Robert Wisbauer, 8-10 September 2006, Porto, Portugal, (Coauthor: E.Toksoy).
- Resolutions in cotorsion theories International Conference on Mathematical Science, 23-27 November 2010 , Bolu Turkey, p.6 (Coauthor: Karen Akıncı).
- The proper classes generated by complements and supplements International Conference on Algebra and Number Theory, Samsun, Turkey, 5 – 8 August 2014, p. 8 – 9.
- Modules with restricted domain of projectivity. International Conference OFSMP-2019, Baku, Azerbaycan, 10-14 June 2019.
- On direct sums of proper classes. Soochow Journal of Math. 23:4(1997), pp. 391-400. (Coauthors: G.Bilhan, A.Pancar)
- Scalar Multiplication of Proper Classes Soochow Journal of Mathematics 30:2(2004), (Coauthors: A.Pancar, B.Sezen)
- The Inductive Closure of Supplements Journal of the Faculty of Science Ege Univ. 27, 2004, p.33-48, http://sci.ege.edu.tr/~jfs/math_2004.html (Coauthor: E.Mermut)
- On the Structure of Neat-Injective Envelopes Mathematica (Cluj) 46(69):2, 2004, (Coauthors: K.Akıncı, A.Imam)
- Proper classes related with complements and supplements Palestine Journal of Mathematics 4(spec.1)(2015), 471-489 (Coauthor: E.Mermut)
- Some properties of inductively closed proper classes in abelian groups. Proc. of Fourth Republ. Conf. of Young Scientists, Baku, 1983.
- Functor lim1 and algebraically compact groups. Proc. of Fifth Republ. Conf. of Young Scientists, Baku, 1984, pp. 3-4.
- Direct sums of proper classes of short exact sequences. VIII. National Math. Symp. Of Turkish Math. Association, Abstracts, Adana, 1995 (Coauthors: G.Bilhan, A.Pancar)
- Modules Sharing a Common Flat Precover. Antalya Algebra Days II, May 17-21, 2000, Abstracts , p.1-2 (Coauthor: K. Akıncı).
- On Cofinitely Supplemented Modules. Antalya Algebra Days II, May 17-21, 2000, Abstracts, p.2-3(Coauthors:G.Bilhan, P.Smith)
- On the Structure of Neat-Injective Envelopes Antalya Algebra Days II, May 17-21, 2000, Abstracts , p.8 (Coauthors: A.Imam. K.Akıncı)
- On λ- and μ- Dimensions of Modules, Antalya Algebra Days VII, 18-22 May 2005 (Coauthor: K.Akıncı).
- On weakly Supplemented Modules Antalya Algebra Days VII, 18-22 May 2005 (Coauthor: E.Büyükaşık).
- The inductive closure of the proper class of supplements in abelian groups, Antalya Algebra Days VII, 18-22 May 2005 (Coauthor: E.Mermut).
- Absolutely supplement modules Antalya Algebra Days VII, 18-22 May 2005 (Coauthor: E.Toksoy).
- Absolutely supplement modules Antalya Algebra Days VII, 18-22 May 2005 (Coauthor: E.Toksoy).
- Amply Cofinitely Supplemented Lattices Antalya Algebra Days VIII, 17-21 May 2006 (Coauthor: E.Toksoy).
- Extensions of weakly supplemented modules Antalya Algebra Days IX, 22-27 May 2007 (Coauthor: E.Büyükaşık).
- Weakly supplemented Lattices Antalya Algebra Days IX, 22-27 May 2007 (Coauthor: E.Toksoy).
- Proper class generated by submodules that have supplements Antalya Algebra Days X, 27-31 May 2008 (Coauthor: Y.Demirci).
- Extensions of weakly supplemented lattices Antalya Algebra Days X, 27-31 May 2008 (Coauthor: E.Toksoy).
- Totally supplemented Modules XXII National Mathematical Symposium, Şirince, İzmir, 30.08 - 03.09.2009, p.49 (Coauthor: Serpil Güngör).
- Cofinitely supplemented Lattices XXII National Mathematical Symposium, Şirince, İzmir, 30.08 - 03.09.2009, p.71 (Coauthor: E.Toksoy)
- On inductively closed proper classes in the category of abelian groups. Unpublished materials deposited at VINITI on 6.12.1982, No. 5971-82 DEP.
- On R1R2 - projective modules. Unpublished materials deposited at VINITI on 6.12.1982 No. 5970-82 DEP (Coauthor: Fedin S.N.).
- Homoloji Cebire Giriş, Samsun, 1999 (Coauthor: A.Pancar)
- Sonlu Matematik, Olimpiyat Soruları ve Çözümleri. TÜBİTAK Yayınları, 2006. (Coauthor: Ü.Ufuktepe).
- Sonlu Matematik, Olimpiyat Soruları ve Çözümleri (updated new edition). Altın Nokta Yayınları, 2011. (Coauthor: Ü.Ufuktepe).
- Sonlu Matematik, Olimpiyat Soruları ve Çözümleri (updated new edition). Altın Nokta Yayınları, 2014. (Coauthor: Ü.Ufuktepe).
- Sonlu Matematik, Olimpiyat Soruları ve Çözümleri (updated new edition). Altın Nokta Yayınları, 2020. (Coauthor: Ü.Ufuktepe).
- Sonlu Matematik, Olimpiyat Soruları ve Çözümleri (updated new edition). Altın Nokta Yayınları, 2022. (Coauthor: Ü.Ufuktepe).
- Matematik Olimpiyatlarına Hazırlık Denemeleri, Altın Nokta Yayınları, 2020. (Coauthors: Murat Şahin, Selçuk Sağbaş, Yunus Al).
- Ortaokul Matematik Olimpiyatlarına Hazırlık Denemeleri, to appear in Altın Nokta Yayınları in 2023 (Coauthors: Murat Şahin, Selçuk Sağbaş, Yunus Al).
- Column "Problemler ve Çözümleri" in the popular mathematical journal "Matematik Dünyası" since 2001.