| Autor: |
Khanjanzadeh, Zeinab, Madanshekaf, Ali |
| Předmět: |
|
| Zdroj: |
Communications in Algebra; 2018, Vol. 46 Issue 5, p1868-1888, 21p |
| Abstrakt: |
Let S be a monoid. In this manuscript, our purpose is to study the notion of weak ideal topology jI on the topos Act-S of all (right) representations of S, where I is a left ideal of S. After a brief analysis of the weak ideal topology, we give a necessary and sufficient condition for a jI-separated S-act to become a jI-sheaf in which the ideal I is central. Moreover, we establish another form of the double negation topology on Act-S which we call the torsion topology. Then, we retrieve the torsion topology on Act-S by means of the internal existential quantifier , in which RIdl(S) is the Heyting algebra of all right ideals of S. Furthermore we give an explicit description of the associated sheaf functor for the ideal topology jI where I is a central band of S; e.g. the ideal ℕ of natural numbers of the monoid (ℕ∞,min) of extended natural numbers. Finally, for certain ideals I we show that the topos of all jI-sheaves is a De Morgan topos provided that the monoid S satisfies in the right Ore condition. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
|
