Constructions of weak inverse property loops

Constructions of Weak Inverse Property Loops

Generating Loops with the Inverse Property

This is an investigation in the tradition of Fujita et al (IJCAI 1993), Zhang et al (JSC 1996), Dubois and Dequen (CP 2001) in which CP or SAT techniques are used to answer existence questions concerning small algebras. In this paper, we open the attack on IP loops, an interesting and underinvestigated variety intermediate between loops and groups.

On Middle Universal Weak and Cross Inverse Property Loops with Equal Lenght of Inveres Cycles

This study presents a special type of middle isotopism under which the weak inverse property (WIP) is isotopic invariant in loops. A sufficient condition for a WIPL that is specially isotopic to a loop to be isomorphic to the loop isotope is established. It is shown that under this special type of middle isotopism, whenever n is a positive even integer, a finite WIPL has an inverse cycle of len...

m at h . G M ] 1 1 Ju n 20 07 On A Pair Of Universal Weak Inverse Property Loops ∗ †

A new condition called T condition is introduced for the first time and used to study a pair of isotopic loops. Under this condition, a loop in the pair is a WIPL if and only if the other loop is a WIPL. Furthermore, such WIPLs are isomorphic. The translation elements f and g of a CIPL with the T condition(such that its f, g-isotope is an automorphic inverse property loop) are found to be alter...

The Weak Lefschetz Property, Inverse Systems and Fat Points

In [13], Migliore–Miró-Roig–Nagel show that the Weak Lefschetz property can fail for an ideal I ⊆ K[x1, . . . , x4] generated by powers of linear forms. This is in contrast to the analogous situation in K[x1, x2, x3], where WLP always holds [16]. We use the inverse system dictionary to connect I to an ideal of fat points, and show that failure of WLP for powers of linear forms is connected to t...