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Let $M$ be a lattice module over a $C$-lattice $L$. Let $Spec^{s}(M)$ be the collection of all second elements of $M$. In this paper, we consider a topology on $Spec^{s}(M)$, called the second classical Zariski topology as a generalization of concepts in modules and investigate the interplay between the algebraic properties of a lattice module $M$ and the topological properties of $Spec^{s}(M)$. We investigate this topological space from the point of view of spectral spaces. We show that $Spec^{s}(M)$ is always $T_{0}-$space and each finite irreducible closed subset of $Spec^{s}(M)$ has a generic point.
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참고문헌 (19)
참고문헌 신청
F. Alarcon / 1995 / Some results on abstract commu-tative ideal theory / Period. Math. Hungar 30(1):1~26
E. A. Al-Khouja / 2003 / Maximal elements and prime elements in lattice modules / Dam-ascus Univ. Basic Sci 19(2):9~21
H. Ansari-Toroghy / 2014 / The Zariski topology on the second spec-trum of a module / Algebra Colloq 21(4):671~688
H. Ansari-Toroghy / 2016 / The Zariski topology on the second spectrum of a module(II) / Bull. Malays. Math. Sci. Soc. 39(3):1089~1103
S. Ballal / 2015 / Zariski topology on lattice modules / Asian-Eur. J. Math. 8(4):10
E. A. Al-Khouja / 2003 / Maximal elements and prime elements in lattice modules / Dam-ascus Univ. Basic Sci 19(2):9~21
H. Ansari-Toroghy / 2014 / The Zariski topology on the second spec-trum of a module / Algebra Colloq 21(4):671~688
H. Ansari-Toroghy / 2016 / The Zariski topology on the second spectrum of a module(II) / Bull. Malays. Math. Sci. Soc. 39(3):1089~1103
S. Ballal / 2015 / Zariski topology on lattice modules / Asian-Eur. J. Math. 8(4):10
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