In abstract algebra, a magmaG is said to be left alternative if (xx)y=x(xy) for all x and y in G and right alternative if y(xx)=(yx)x for all x and y in G. A magma that is both left and right alternative is said to be alternative.
Any associative magma (semigroup) is clearly alternative. More generally, a magma in which every pair of elements generates an associative submagma must be alternative. The converse, however, is not true, in contrast to the situation in alternative algebras. In fact, an alternative magma need not even be power-associative.
Alternative rock was played extensively on the radio in the UK, particularly by DJs such as John Peel (who championed alternativemusic on BBC Radio 1), Richard Skinner, and Annie Nightingale.
While "alternative" was simply an umbrella term for a diverse collection of underground rock bands, Nirvana and similar groups gave it a reputation for being a distinct style of guitar based rock which combined elements of punk and metal; their creation met with considerable commercial success.
The explosion of alternative rock was aided by MTV and Lollapalooza, a touring festival of diverse bands which helped expose and popularizealternative groups such as Nine Inch Nails, The Smashing Pumpkins, and Hole.
Alternative pop/rock is essentially a catch-all term for post-punk bands from the mid-'80s to the mid-'90s.
There is a multitude of musical styles within alternative rock, from the sweet melodies of jangle-pop to the disturbing metallic grind of industrial, yet are all tied together by a similar aesthetic -- they all existed and operated oustide of the mainstream.
Throughout the '80s, the majority of alternativebands were on independent labels; those that eventually signed to major labels, such as Hüsker Dü and the Replacements, didn't break through to the mainstream and thereby were able to keep their hip credentials alive.