**Serban
Raianu**

**Professional
experience:** Professor, Department Chair (2006-2008), California State
University Dominguez Hills, 2004-present, Associate Professor, California State
University Dominguez Hills, 2002-2004, Visiting Associate Professor, Syracuse University, 2000-2002,
Associate Professor, University of Bucharest, 1996-2000, Assistant Professor,
University of Bucharest, 1992-1995, Instructor, University of Bucharest
1988-1992.

**Ph.D.
thesis:** "New contributions to the structure of graded rings
and modules", 1991, University of Bucharest, supervisor Constantin Năstăsescu.

**Current
scientific interests: **Hopf
algebras acting on algebras and coalgebras, Quantum Groups.

**International Conferences:** Bressanone, Italy (1990), Ramat Gan, Israel (1991), Chicago
(1992), Antwerp, Belgium (1996), Saint John's, Canada (1997), Brussels, Belgium
(1998), Berkeley (1999) (a video of the lecture is available at http://www.msri.org/publications/ln/msri/1999/hopfalg/raianu/1/),
Chicago (2002), New York (2003), Haifa (2004), Santa Barbara (2005), Saint
John's, Canada (2009), Sde Boker,
Israel (2010), Bucharest, Romania (2013), Halifax, Canada (2014), Iasi, Romania
(2015).

**Invited
Lectures: **

Brussels, Belgium (1990, 1991, 1992, 1993, 1994, 1995, 1996,
1998), Antwerp, Belgium (1990, 1991, 1992, 1993, 1994, 1995, 1996, 1998), Hasselt, Belgium (1994, 1996, 1998), Beer
Sheva, Israel (1992), Ferrara, Italy (1997), Padova, Italy (1997), Murcia,
Spain (1998), University of Southern California (2001), University of Illinois
at Chicago (2001), University of New Mexico, Albuquerque (2003), El Camino
College, Torrance (2004), Cal Poly Pomona (2004), Cal State San Bernardino
(2006), Cal State Channel Islands (2007), DePaul University (2011), Cal State
Channel Islands (2013) ), Bucharest (2014).

**Courses
taught:**

Beginning Algebra, Intermediate Algebra, Mathematics for
Elementary School Teachers: Real Numbers, , Mathematics for Elementary School
Teachers: Geometry and Probability, CSET I and II Content Course, Precalculus,
Calculus I, II, III, Linear Algebra, Abstract Algebra, Number Theory, Complex
Analysis, Probability and Statistics, General Algebra, Algebra and Arithmetic,
Modern techniques in elementary mathematics, Algebra and Analytic Geometry,
Geometry, Lie algebras, Algebras and coalgebras, Representation theory of
finite dimensional algebras, Graded rings and modules, Applications of group
theory. Systematically involved in teacher preparation.

**Grants,
Prizes, and Other Activities:**

- First prize in the 1981 annual scientific
contest for students at the University of Bucharest. Title of paper: "The
Cousin complex".

- Gheorghe Titeica prize of the Romanian Academy, 2001.

- Guest researcher
University of Antwerp 1995-1996.

- Visiting professor
Ferrara (February 1997).

- Two grants from the
Romanian Academy of Science (coordinator) 1994, 1995.

- Research project joint
with the Universities of Antwerp, Brussels, Hasselt, all Belgium, (participant)
1996-1999.

- Campus coordinator for
the Louis Stokes Alliance for Minority Participation, NSF-Cal State grant, 2003-2006.

- PUMP Undergraduate
Research Grant 2016-2017 (with Natalia da Silva and Hector Salgado).

- Math Alliance Mentor.

- California Math Alliance
Mentor.

- Reviewer for Zentralblatt für Mathematik and Mathematical Reviews.

- Member of the AMS.

- Member of the AWM.

- Member of the NAM.

- Co-organizer (with Gizem Karaali and Susan
Montgomery) of AMS special section Hopf Algebras and
Quantum Groups, Claremont McKenna, 2008.

- Co-organizer (with Davida
Fischman) of MAA Invited Paper Session Topics in Hopf Algebras, Joint Meetings, New Orleans, 2011.

- Editorial Board ISRN
Algebra, 2011-present, journal website: http://www.isrn.com/journals/algebra/

- Editorial Board Algebra
Letters, 2012-present, journal website: http://scik.org/index.php/abl/

- Managing Editor PUMP
Journal of Undergraduate Research, 2017-present, journal website: https://math.csudh.edu/pumpjournal

**List
of publications:**

**Books:**

1. Structuri algebrice,
Tipografia Univ. Buc., 1981 (with I. D. Ion and C. Manoil).

2. Lecţii de Algebră Comutativă, Tipografia Univ.
Buc., 1984 (with T. Albu).

3. Algebre Hopf,Tipografia
Univ. Buc. 1999 (with S. Dăscălescu and C. Năstăsescu).

4. Hopf Algebras: an Introduction,
Marcel Dekker Monographs and Textbooks, vol. 235, 2001 (with S. Dăscălescu and C. Năstăsescu).

**Papers
(published or accepted):**

1. Cousin complex, local cohomology
and torsion theory, Communications in Algebra, 9(16) 1982, 691-1720 (with T. Albu).

2. Gabriel dimension of graded rings, Rend. Sem. Mat. Univ.
Padova, 71 (1984), 195-208 (with C. Năstăsescu).

3. Stability conditions for commutative rings with Krull
dimension, Methods in Ring Theory, Reidel 1984,
391-402 (with C. Năstăsescu).

4. Finiteness conditions for graded modules (gr-∑(∆)-injective modules), Journal of Algebra, 100
(1) 1986, 179-190 (with C. Năstăsescu).

5. A remark on strongly graded rings with finiteness
conditions, Bull. Math. Soc. Math. Roumanie, 30 (78)
1986, 265-269.

6. External homogeneization for
finitely generated abelian groups, Ann. Univ. Ia\c{s}i, XXX, 1985, 58-60 (with C. Năstăsescu).

7. Gabriel dimension of graded rings II, Journal of Pure and
Applied Algebra, 50 (1988), 73-79 (with C. Năstăsescu).

8. Cousin complex characterization of non-noetherian n-Gorenstein rings,
Communications in Algebra, 15 (7), 1987, 1533-1541.

9. Modules graded by G-sets, Mathematische
Zeitschrift, 203 (1990), 605-627 (with C. Năstăsescu and F. Van Oystaeyen).

10. Induction and coinduction for Hopf algebras, Journal of Algebra, 165, 1994, 204-222,
(with S. Caenepeel and F. Van Oystaeyen).
pdf

11. Semiinvariants for Hopf
algebra actions, Israel Journal of Mathematics, 88, 1994, 279-306 (with M.
Cohen and S. Westreich).

12. Graded Coalgebras and Morita-Takeuchi Contexts, Tsukuba
Journal of Mathematics, 19 (1995) 395-407 (with S. Dăscălescu,
C. Năstăsescu and F. Van Oystaeyen).

13. Finite Hopf-Galois
Coextensions, Crossed Coproducts and Duality, Journal of Algebra, 178 (1995)
400-413 (with S. Dăscălescu and Y. Zhang).

14. Coinduction for infinite
dimensional Hopf algebras, Journal of Pure and Applied Algebra,
107 (1996) 141-151 (with S. Caenepeel and B. Zhou).

15. A Maschke-type theorem for
crossed coproducts, Analele Univ. Constanţa,
2 (1994), 44-51 (with S. Caenepeel and S. Dăscălescu).

16. Cosemisimple Hopf algebras coacting on coalgebras, Communications
in Algebra, 24 (1996), 1649-1677 (with S. Caenepeel
and S. Dăscălescu).

17. Induction functors for the Doi-Koppinen
unified Hopf modules, in Abelian groups and modules,
Proceedings of the Padova Conference, Padova, Italy, June 23-July 1, 1994,
Kluwer, 1995, eds. A. Facchini and C. Menini, p. 73-94., (with S. Caenepeel)
pdf

18. Cleft coextensions and crossed coproducts,
Communications in Algebra, 24 (1996), 1229-1243 (with S. Dăscălescu
and G. Militaru).

19. Strongly graded coalgebras and crossed coproducts (with S. Dăscălescu and C. Năstăsescu),
in Abelian Groups, Module Theory and Topology, Proceedings of the fourth week
on algebra and algebraic geometry, eds. S. Caenepeel,
A. Verschoren, Marcel Dekker Lecture Notes in Pure
and Appl. Math., vol. 197, 1998, 103-110.

20. Smash (Co)products from Adjunctions, (with S. Dăscălescu and F. Van Oystaeyen),
Hopf Algebras, and Brauer
Groups, Proceedings in honour of Adalberto Orsatti's 60th birthday, eds. D. Dikranjan,
L. Salce, Marcel Dekker Lecture Notes in Pure and
Appl. Math., vol. 201, 1998, 131-142.

21. Some remarks on a theorem of H.-J. Schneider, Communications in Algebra, 24 (1996),
4477-4493 (with S. Dăscălescu
and F. Van Oystaeyen).

22. Galois extensions for co-Frobenius
Hopf algebras (with M. Beattie and S. Dăscălescu),
J. Algebra, 198 (1997), 164-183.

23. The Categories of Yetter-Drinfel'd
Modules, Doi-Hopf Modules and Two-sided Two-cosided Hopf Modules,(with M. Beattie, S. Dăscălescu
and F. Van Oystaeyen), Applied Categorical
Structures, 6 (1998), 223-237.

24. Morphisms of Relative Hopf
Modules, Smash Products and Duality, (with C. Menini),
J. Algebra 219 (1999) 547-570.

25. Classifying pointed Hopf
algebras of dimension 16, (with S. Dăscălescu and S. Caenepeel),
Comm. Algebra 28 (2000), 541-568.

26. An easy proof of the uniqueness of integrals, in Hopf Algebras and Quantum Groups, Proceedings of the
Brussels Conference 1998, (eds. S. Caenepeel and F.
Van Oystaeyen), Marcel Dekker Lecture Notes in Pure
and Appl. Math., vol 209, 2000, 237-240.

27. Co-Frobenius Hopf algebras with a separable Hopf-Galois
extension are finite dimensional, (with M. Beattie and S. Dăscălescu),
Proceedings of the AMS 128, nr. 11 (2000), 3201-3203.

28. Finite Hopf-Galois extension
equivalent to crossed products (with M. Saorín),
Comm. Algebra 29 (2001), 4871-4882.

29. Semiprime crossed products over copointed
Hopf algebras, (with D. Quinn), Proceedings of the
AMS 131 (2003), 29-33.

30. Lifting of Nichols algebras of type B_{2} (with M. Beattie and
S. Dăscălescu), with an appendix "A
generalization of the q-binomial theorem", with I. Rutherford, Israel J. of Math 132 (2002), 1-28.

31. Coalgebras from formulas, in Hopf
Algebras, Proceedings
of the International Conference on Hopf Algebras held
at DePaul University, Chicago, Illinois, edited by Jeff Bergen, Stefan Catoiu, William Chin, Lecture Notes In Pure and Applied
Mathematics, Vol. 237, Marcel Dekker,
2004, 215-224. pdf

32. Does the Jordan Form of a Matrix have the Maximum Number
of Zeros? (with F. Brulois and G. Jennings), Bull. Math.Soc. Sc. Math. Roumanie Tome
48(96) No. 4, 2005, 359-360. pdf

33. Duality for Finite Hopf
Algebras explained by Corings, (with S. Caenepeel and D. Quinn), Applied Categorical Structures 14 (2006),
no. 5-6, 531-537. pdf

34. Balanced bilinear forms for corings (with M. Beattie and D. Bulacu),
"Modules and Comodules" Proceedings of a conference dedicated to Robert
Wisbauer, Trends in Mathematics, 87-99, 2008, Birkhäuser, (Editors: Tomasz Breziński,
José Luis Gomez Pardo, Ivan Shestakov, Patrick
Smith). pdf

35.
The antipode of a dual quasi-Hopf algebra with
non-zero integrals is bijective (with M. Beattie and M.C. Iovanov),
Algebras and Representation Theory 12 (2009), no. 2-5, 251-255. pdf

36.
The bijectivity of the antipode revisited (with M.C. Iovanov),
Comm. Algebra 39 (2011), no. 12, 4662–4668. pdf

37.
Stable equivalences of Morita type and Frobenius
extensions (with M. Beattie and S. Caenepeel), Annals
of The Univ. of Bucharest (mathematical series) 2 (LX) (2011), 123-126. pdf

38. External
homogenization for Hopf algebras: a coring point of
view, Bull. Math. Soc. Sci. Math. Roumanie (NS)
56(104) (2013), no. 3, 369–375.

39. Arithmetic properties of 3-cycles of quadratic maps over ℚ (with
Patrick Morton), J. Number Theory, 240 (2022), 685-729. (see
https://arxiv.org/abs/2105.07435
)

**Expository
articles:**

1. Module Cohen-Macaulay, in Seminar de Algebră,
Univ. Iaşi, 1986.

2. Smash products and applications, Proceedings of the
Algebra Conference, Braşov, 1988 (with C. Năstăsescu).

3. Crossed coproducts, Proceedings of the International
Conference on Representation Theory, Constanţa,
1995.

4. The Integral of Secant and Stereographic Projections of
Conic Sections (with George Jennings, David Ni, Wai Yan Pong), https://arxiv.org/abs/2204.11187

**Undergraduate
Student Research Projects:**

1.
Computing areas using Green’s Theorem and a Software
Planimeter, (with Paul Davis) Teaching Mathematics Applications 2007, Volume
26, Number 2, 103-108, Oxford University Press, pdf

2.
Differences of Harmonic Numbers and the abc-Conjecture,
(with Natalia da Silva and Hector Salgado), PUMP J. Undergrad. Res., 1 (2018),
1-13. pdf

3.
Partition Problems and a Pattern of Vertical Sums, (with
Eunice Krinsky and Alexander Wittmond),
PUMP J. Undergrad. Res., 1 (2018), 30-47. pdf