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For the question ``when is $E(_RR)$ a flat left $R$-module for any ring $R$?", in this paper, we deal with a class of modules partaking in the hierarchy of injective and cotorsion modules, so-called Harmanci injective modules, which turn out by the motivation of relations among the concepts of injectivity, flatness and cotorsionness. We give some characterizations and properties of this class of modules. It is shown that the class of all Harmanci injective modules is enveloping, and forms a perfect cotorsion theory with the class of modules whose character modules are Matlis injective. For the objective we pursue, we characterize when the injective envelope of a ring as a module over itself is a flat module.
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참고문헌 (16)
참고문헌 신청
L. BICAN / 2001 / ALL MODULES HAVE FLAT COVERS / Bulletin of the London Mathematical Society 33(4):385~390
E. E. Bray / 1971 / The Injective Envelope of the Upper Triangular Matrix Ring / The American Mathematical Monthly 78(8):883~886
Nanqing Ding / 2011 / On envelopes with the unique mapping property / Communications in Algebra 24(4):1459~1470
Paul C Eklof / 1991 / On Whitehead modules / Journal of Algebra 142(2):492~510
Edgar E. Enochs / 1981 / Injective and flat covers, envelopes and resolvents / Israel Journal of Mathematics 39(3):189~209
E. E. Bray / 1971 / The Injective Envelope of the Upper Triangular Matrix Ring / The American Mathematical Monthly 78(8):883~886
Nanqing Ding / 2011 / On envelopes with the unique mapping property / Communications in Algebra 24(4):1459~1470
Paul C Eklof / 1991 / On Whitehead modules / Journal of Algebra 142(2):492~510
Edgar E. Enochs / 1981 / Injective and flat covers, envelopes and resolvents / Israel Journal of Mathematics 39(3):189~209
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