Photovoltaic system in northern climes to 5.61 kWh/m²/day in the sunniest regions. For large systems, the energy gained by using tracking systems can outweigh the added complexity (trackers can increase efficiency by 30% or more). For very large systems, the added maintenance of tracking is a substantial detriment. Tracking is not required for flat panel and low-concentration photovoltaic systems. For high-concentration photovoltaic systems, dual axis tracking is a necessity. Pricing trends affect the balance between adding more stationary solar panels versus having fewer panels that track. When solar panel prices drop, trackers become a less attractive option. Systems designed to deliver alternating
Injective module proved a useful result, usually known as Baer's Criterion, for checking whether a module is injective: a left "R"-module "Q" is injective if and only if any homomorphism "g" : "I" → "Q" defined on a left ideal "I" of "R" can be extended to all of "R". Using this criterion, one can show that Q is an injective abelian group (i.e. an injective module over Z). More generally, an abelian group is injective if and only if it is divisible. More generally still: a module over a principal ideal domain is injective if and only if it is divisible