# User:Krishnachandranvn

In mathematics, a Rees matrix semigroup is a special semigroup whose elements can be thought of as matrices over some semigroup with zero, and whose rows and columns are indexed by some arbitrary nonempty sets. The binary operation in the semigroup makes use of a special sandwich matrix defined over the same semigroup with zero. The special case of such semigroups where the elements are selcted from a group with zero has some important properties. This special case and its properties were first studied by D Rees in a paper published in 1940.

## Definition

Let S be a semigroup with zero, let Ι and Λ be two nonempty indexing sets and P a Λ × Ι matrix over S. Let M be the set of all Ι × Λ matrices over S having the property that in each matrix exactly one element is nonzero. For A and B in M if we let A $\circ$ B = APB, where the right hand side expression is the usual product of matrices, then " $\circ$ " defines a binary operation in M. With this operation, M becomes a semigroup and it is called a Rees matrix semigroup. The commonly used notation for this semigroup is M(S; Ι, Λ; P). To be more specific, let the notation A = (a)pq indicate the fact that the only nonzero element of A is a and that this nonzero element appears in the p-th row and q-th column of A. Then the binary operation in M can be specified as

(a)i λ $\circ$ (b)j μ = (a pλ j b)i μ

for a, bS \ {0}, i, j ∈ Ι, and λ, μ ∈ Λ.

## Editions of Kerala Science Congress

Serial Number Year Dates Theme Place where held
1 1989 N. Balakrishnan Nair Natural resources & industrial development of Kerala Cochin University of Science & Technology
2 1990 N. Balakrishnan Nair Thiruvananthapuram
3 1991 N Balakrishnan Nair Thiruvananthapuram
4 1992 C G Ramachandran Nair Thrissur
5 1993 R Ravi Kumar Kottayam
6 1994 Thiruvananthapuram
7 1995 Example Example Example
8 1996 Iyengar, P.K. Example Example
9 1997 Example Example Example
10 1998 Example Example Example
11 1999 Example Example Idukki
12 2000 Example Example Example
13 2001 Example Example Example
14 2002 Example Example Example
15 2003 M S Valiathan Example Thiruvananthapuram
16 2004 Example Example Example
17 2005 Example Example Example
18 2006 Example Example Example
19 2007 Example Example Example
20 2008 Example Example Example
21 2009 Example Example Example
22 2010 Example Example Example
23 2011 Example Example Example
24 2012 Example Example Rubber Research Institute of India, Kottayam
25 2013 Example Example Example
26 2014 Example Example Example