31 خرداد 1403
سعيد باقري (بازنشسته)

سعید باقری (بازنشسته)

مرتبه علمی: استادیار
نشانی: ملایر-کیلومتر 4 جاده اراک-دانشگاه ملایر- دانشکده علوم ریاضی- گروه ریاضی
تحصیلات: دکترای تخصصی / ریاضی جبر
تلفن:
دانشکده: دانشکده علوم ریاضی و آمار

مشخصات پژوهش

عنوان
Distributive lattices and some related topologies in comparison with zero-divisor graphs
نوع پژوهش مقاله چاپ شده
کلیدواژه‌ها
Distributive lattice, Goldie dimension, compressed zero-divisor graph, domination number.
سال
2021
مجله categories and general algebraic structures with applications
پژوهشگران سعید باقری (بازنشسته)

چکیده

In this paper, for a distributive lattice L, we study and compare some lattice theoretic features of L and topological properties of the Stone spaces Spec(L) and Max(L) with the corresponding graph theoretical aspects of the zero-divisor graph \Gamma(L). Among other things, we show that the Goldie dimension of L is equal to the cellularity of the topological space Spec(L) which is also equal to the clique number of the zero-divisor graph \Gamma(L). Moreover, the domination number of \Gamma(L) will be compared with the density and the weight of the topological space Spec(L). For a 0-distributive lattice L, we investigate the compressed subgraph E(L) of the zero-divisor graph \Gamma(L) and determine some properties of this\Gamma_ subgraph in terms of some lattice theoretic objects such as associated prime ideals of L.