Fir

Firs (Abies) are a genus of 48–56 species of evergreen coniferous trees in the family Pinaceae. They are found through much of North and Central America, Europe, Asia, and North Africa, occurring in mountains over most of the range. Firs are most closely related to the genus Cedrus (cedar). Douglas firs are not true firs, being of the genus Pseudotsuga.

They are large trees, reaching heights of 10–80 m (33–262 ft) tall and trunk diameters of 0.5–4 m (1 ft 8 in–13 ft 1 in) when mature. Firs can be distinguished from other members of the pine family by the unique attachment of their needle-like leaves and by their different cones.

Identification of the different species is based on the size and arrangement of the leaves, the size and shape of the cones, and whether the bract scales of the cones are long and exserted, or short and hidden inside the cone.

Leaves

Firs can be distinguished from other members of the pine family by the unique attachment of their needle-like leaves to the twig by a base that resembles a small suction cup.

Free ideal ring

In mathematics, especially in the field of ring theory, a (right) free ideal ring, or fir, is a ring in which all right ideals are free modules with unique rank. A ring such that all right ideals with at most n generators are free and have unique rank is called an n-fir. A semifir is a ring in which all finitely generated right ideals are free modules of unique rank. (Thus, a ring is semifir if it is n-fir for all n ≥ 0.) The semifir property is left-right symmetric, but the fir property is not.

Properties and examples

It turns out that a left and right fir is a domain. Furthermore, a commutative fir is precisely a principal ideal domain, while a commutative semifir is precisely a Bézout domain. These last facts are not generally true for noncommutative rings, however (Cohn 1971).

Every principal right ideal domain R is a right fir, since every nonzero principal right ideal of a domain is isomorphic to R. In the same way, a right Bézout domain is a semifir.

Since all right ideals of a right fir are free, they are projective. So, any right fir is a right hereditary ring, and likewise a right semifir is a right semihereditary ring. Because projective modules over local rings are free, and because local rings have invariant basis number, it follows that a local, right hereditary ring is a right fir, and a local, right semihereditary ring is a right semifir.

USCGC Fir (WLM-212)

The United States Coast Guard Cutter Fir (WAGL/WLM 212) was the last lighthouse tender built specifically for the United States Lighthouse Service to resupply lighthouses and lightships, and to service buoys. Fir was built by the Moore Drydock Company in Oakland, California in 1939. On 22 March 1939, the U.S. Lighthouse Tender Fir was launched. She was steam driven with twin screws, 175 feet (53 m) in length, had a beam of 32 feet (9.8 m), drew 11 feet 3 inches (3.43 m) of water, and displaced 885 tons. Fir was fitted with a reinforced bow and stern, and an ice-belt at her water-line for icebreaking. She was built with classic lines and her spaces were lavishly appointed with mahogany, teak, and brass. The crew did intricate ropework throughout the ship. The cost to build Fir was approximately US$390,000. Fir's homeport was Seattle, Washington for all but one of her fifty one years of service when she was temporarily assigned to Long Beach, California when USCGC Walnut was decommissioned on 1 July 1982.