- published: 10 Jun 2014
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In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. The binary operation of a semigroup is most often denoted multiplicatively: x·y, or simply xy, denotes the result of applying the semigroup operation to the ordered pair (x, y). Associativity is formally expressed as that (x·y)·z = x·(y·z) for all x, y and z in the semigroup.
The name "semigroup" originates in the fact that a semigroup generalizes a group by preserving only associativity and closure under the binary operation from the axioms defining a group. From the opposite point of view (of adding rather than removing axioms), a semigroup is an associative magma. As in the case of groups or magmas, the semigroup operation need not be commutative, so x·y is not necessarily equal to y·x; a typical example of associative but non-commutative operation is matrix multiplication. If the semigroup operation is commutative, then the semigroup is called a commutative semigroup or (less often than in the analogous case of groups) it may be called an abelian semigroup.
Complete set of Video Lessons and Notes available only at http://www.studyyaar.com/index.php/module/1-algebraic-structures-groups-and-rings n-ary operation, Algeraic System, Binary Operations, Semi-Group, Residue Class Modulo n, Identity, Monoid http://www.studyyaar.com/index.php/module-video/watch/81-algebraic-system-basic-concepts-semi-group-identity-element-and-monoids
PROGRAM NAME :WINTER SCHOOL ON STOCHASTIC ANALYSIS AND CONTROL OF FLUID FLOW DATES Monday 03 Dec, 2012 - Thursday 20 Dec, 2012 VENUE School of Mathematics, Indian Institute of Science Education and Research, Thiruvananthapuram Stochastic analysis and control of fluid flow problems have seen great mathematical advancement over past two decades. A vast number of physical and engineering systems are encompassed under various flow governing equations. Various applications lie in defense related problems, important one is aero-hydrodynamic drag reduction in aerial, surface and undersea vehicles. Other applications are in atmospheric and ocean data assimilation, plasma fusion and energy-environmental problems. The aim of the school is to make students and researchers across various organiza...
Ninth lecture in abstract algebra. Topics include magmas, semigroups, monoids, homomorphisms, and isomorphisms. This lecture is in four parts.
Theorem: A regular semigroup is inverse if and only if its idempotents commute. A fascinating and beautiful result, true classics, having a nice and elegant proof. It was first proved in 1950's I think, by a Russian pioneer in inverse semigroup theory, V. V. Vagner. But I think it was also proved by some mathematician in U. S. independently (I read about it long time ago). Sorry in advance for a little bit awkward word usage in English, it's not my first language, and sorry for using a lot of "a times b" instead of "a multiplied by b" what it should've been. "a times b" doesn't have much sense in semigroup theory, but I used it because in Estonian, "a times b" is "a korda b" which is normal usage also in semigroup theory, and "a multiplied by b" is "a korrutatud b-ga", which is so awkwar...
9 Semigroups of linear operators - Strongly continuous semigroups and Resolvents
Situation died, hopelessness arrived
Was it just a game you played,
to see if you could manage
Pushed me into something,
that I could not reach you
And I'm too scared to try
If only you could tell me,
that you couldn't stand me
Then I would keep to my part of the world
But memories won't leave me and I really think you care
Picked up the phone and tried to
hear you through the open line
But I forgot your number and
you never knew mine
Looking for something to believe in,
but nothing really matter anymore but love
A distant happiness all gone in helplessness
Have I lived it all