Azarang, A.; Karamzadeh, Omid Ali Shahni Which fields have no maximal subrings? (English) Zbl 1234.13009 Rend. Semin. Mat. Univ. Padova 126, 213-228 (2011). The authors determine completely fields which have no maximal subrings. Reviewer: Marius Tărnăuceanu (Iaşi) Cited in 2 ReviewsCited in 11 Documents MSC: 13A99 General commutative ring theory Keywords:rings; fields; maximal subrings × Cite Format Result Cite Review PDF Full Text: DOI EuDML Link References: [1] M. F. ATIYAH - I. G. MACDONALD, Introduction to Commutative Algebra, (Addison-Wesley, 1969). · Zbl 0175.03601 [2] A. AZARANG, On maximal subrings, (FJMS) 32 (2009), pp. 107-118. · Zbl 1164.13004 [3] A. AZARANG - O. A. S. KARAMZADEH, On the existence of maximal subrings in commutative artinian rings, J. Algebra Appl., 9 (5) (2010), pp. 771-778. · Zbl 1204.13008 · doi:10.1142/S0219498810004208 [4] A. AZARANG - O. A. S. KARAMZADEH, On Maximal Subrings of Commutative Rings, to appear in Algebra Colloquium (2011). [5] H. E. BELL - F. GUERRIERO, Some Condition for Finiteness and Commu- tativity of Rings. Int. J. Math. Math. Sci., 13 (3) (1990), pp. 535-544. · Zbl 0711.16011 · doi:10.1155/S0161171290000771 [6] H. E. BELL - A. A. KLEIN, On finiteness of rings withfinite maximal subrings. J. Math. Math. Sci., 16 (2) (1993), pp. 351-354. · Zbl 0798.16009 · doi:10.1155/S0161171293000420 [7] J. V. BRAWLEY - G. E. SCHNIBBEN, Infinite algebraic extensions of finite fields (Contemporary mathemathics, 1989). · Zbl 0674.12009 [8] D. FERRAND - J.-P. OLIVIER, Homomorphismes minimaux danneaux, J. Algebra, 16 (1970), pp. 461-471. [9] W. FULTON, Algebraic curves (Benjamin, New York, 1969). · Zbl 0181.23901 [10] R. HARTSHORNE, Algebraic geometry (Graduate Texs in Math. 52, Springer- Verlag, New York-Heidelberg-Berlin, 1977). [11] N. JACOBSON, Lecture in Abstract Algebra III, Theorey of Fields and Galois Theory (Graduate Text in Mathematics 32, Springer-Verlag, New York, 1964). [12] I. KAPLANSKY, Commutative Rings, Revised edn (University of Chicago Press, Chicago 1974). [13] A. A. KLEIN, The Finiteness of a ring with a finite maximal subrings, Comm. Algebra, 21 (4) (1993), pp. 1389-1392. · Zbl 0793.16009 · doi:10.1080/00927879308824626 [14] T. J. LAFFEY, A finiteness theorem for rings, Proc. Roy. Irish Acad. Seet. A, 92 (2) (1992), pp. 285-288. · Zbl 0792.16005 [15] T. Y. LAM, A First Course in Noncmmutative Rings, Second edn, (Springer- Verlag, 2001). [16] T. KWEN LEE - K. SHAN LIU, Algebra witha finite-dimensional maximal subalgebra. Comm. Algebra, 33 (1) (2005), pp. 339-342. · Zbl 1072.16020 · doi:10.1081/AGB-200041024 [17] M. L. MODICA, Maximal subrings, Ph.D. Dissertation. (University of Chicago, 1975). [18] S. ROMAN, Field Theory, Second edn. (Springer-Verlag, 2006). [19] H. STICHTENOTH, Algebraic Function Fields and Codes, Second edn, (Spring- er-Verlag, Berlin Heidelberg, 2009). · Zbl 1155.14022 · doi:10.1007/978-3-540-76878-4 [20] G. D. VILLA SALVADOR, Topics in the Theory of Algebraic Function Fields, (Brikhauser Boston, 2006). · Zbl 1154.11001 [21] C. WEIR, Hyperelliptic function fields, Proceedings of Ottawa Mathematics Conference, May (1-2), (2008). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.