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Recently, Anderson and Dumitrescu's $S$-finiteness has attracted the interest of several authors. In this paper, we introduce the notions of $S$-finitely presented modules and then of $S$-coherent rings which are $S$-versions of finitely presented modules and coherent rings, respectively. Among other results, we give an $S$-version of the classical Chase's characterization of coherent rings. We end the paper with a brief discussion on other $S$-versions of finitely presented modules and coherent rings. We prove that these last $S$-versions can be characterized in terms of localization.
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참고문헌 (9)
참고문헌 신청
H. Ahmed / 2015 / S-Noetherian rings of the forms A[X] and A[[X]] / Comm. Algebra 43(9):3848~3856
H. Ahmed / 2016 / Modules satisfying the S-Noetherian property and S-ACCR / Comm. Algebra 44(5):1941~1951
D. D. Anderson / 2002 / S-Noetherian rings / Comm. Algebra 30(9):4407~4416
D. D. Anderson / 1995 / Agreeable domains / Comm. Algebra 23(13):4861~4883
D. L. Costa / 1994 / Parameterizing families of non-Noetherian rings / Comm. Algebra 22(10):3997~4011
H. Ahmed / 2016 / Modules satisfying the S-Noetherian property and S-ACCR / Comm. Algebra 44(5):1941~1951
D. D. Anderson / 2002 / S-Noetherian rings / Comm. Algebra 30(9):4407~4416
D. D. Anderson / 1995 / Agreeable domains / Comm. Algebra 23(13):4861~4883
D. L. Costa / 1994 / Parameterizing families of non-Noetherian rings / Comm. Algebra 22(10):3997~4011
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