Abstract
This paper introduces the notions of \(K^r\)-faithfulness and quasi-flatness. They are used to discuss non-singularity and Hattori-torsion-freeness in the context of endomorphism rings. Several additional examples are given.
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References
Albrecht, U.: Faithful abelian groups of infinite rank. Proc. Amer. Math. Soc. 103, 21–26 (1988)
Albrecht, U.: Endomorphism rings and a generalization of torsion-freeness and purity. Commun. Algebra 17(5), 1101–1135 (1989)
Albrecht, U.: Abelian groups, A, such that the category of A-solvable groups is preabelian. Contemp. Math. 87, 117–131 (1989)
Albrecht, U.: Two-sided essential submodules of \(Q^r(R)\). Houston J. Math. 33(1), 103–123 (2007)
Albrecht, U.: Non-singular rings of injective dimension \(1\), pp. 421–430. Models, Modules and Abelian Groups, De Gruyter (2008)
Albrecht, U., Dauns, J., Fuchs, L.; Torsion-freeness and non-singularity over right p.p.-rings. J. Algebra 285, 98–119 (2005)
Albrecht, U., Friedenberg, S.: Murley Groups and the torsion-freeness of Ext. J. Algebra 331, 378–387 (2011)
Albrecht, U., Goeters, H.P.: Flatness and the ring of quasi-endomorphisms. Quest. Math. 19, 379–396 (1996)
Albrecht, U., Goeters, H.P.: Strong S-groups. Colloq. Math. 80, 97–105 (1999)
Arnold, D.M., Lady, L.: Endomorphism rings and direct sums of torsion-free Abelian groups. Trans. Amer. Math. Soc. 211, 225–237 (1975)
Arnold, D.M., Murley, C.E.: Abelian groups, \(A\), such that \({\text{ Hom }}(A)\)-preserves direct sums of copies of \(A\). Pac. J. Math. 56, 7–20 (1975)
Baer, R.: Abelian groups without elements of finite order. Duke J. Math. 3, 68–122 (1937)
Chatters, A.W., Hajarnavis, C.R.: Rings with Chain Conditions, vol. 44. Pitman Advanced Publishing, Boston, London, Melbourne (1980)
Dauns, J., Fuchs, L.: Torsion-freeness for rings with zero-divisors. J. Algebra Appl. 3, 221–238 (2004)
Dubois, D.W.: Cohesive groups and p-adic integers. Publ. Math. Debrecen 12, 51–58 (1965)
Faticoni, T.: Each countable reduced torsion-free commutative ring is a pure subring of an \(E\)-ring. Comm. Algebra 15(12), 2545–2564 (1987)
Fuchs, L.: Abelian Groups. Springer (2015)
Fuchs, L., Saclce, L.: Modules over Non-Noetherian domains. Amer. Math. Soc. Monogr. 84, (2000)
Goodearl, K.: Ring Theory. Marcel Dekker, New York, Basel (1976)
Hattori, A.: A foundation of torsion theory for modules over general rings. Nagoya Math. J. 17, 147–158 (1960)
McQuaig, B.; Morita-equivalence between strongly non-singular rings and the structure of the maximal ring of quotients. Dissertation, Auburn University (2017)
Stenström, B.; Rings of Quotients. Lecture Notes in Mathematics, vol. 217. Springer Verlag, Berlin, Heidelberg, New York (1975)
Ulmer, F.: A flatness criterrion in Groethendick categories. Invent. Math. 19, 331–336 (1973)
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Albrecht, U., McQuaig, B. (2019). Hattori-Torsion-Freeness and Endomorphism Rings. In: Feldvoss, J., Grimley, L., Lewis, D., Pavelescu, A., Pillen, C. (eds) Advances in Algebra. SRAC 2017. Springer Proceedings in Mathematics & Statistics, vol 277. Springer, Cham. https://doi.org/10.1007/978-3-030-11521-0_1
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