In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m × n matrix of refined labels are introduced and studied. We mainly study this to introduce to super vector space of refined labels using matrices. We in this book introduce the notion of semifield of refined labels using which we define for the first time the notion of supersemivector spaces of refined labels. Several interesting properties in this direction are defined and derived.
We suggest over hundred problems some of which are simple some at research level and some difficult. We give some applications but we are sure in due course when these new notions become popular among researchers they will find lots of applications. This book has five chapters. First chapter is introductory in nature, second chapter introduces super matrices of refined labels and algebraic structures on these supermatrices of refined labels. All possible operations are on these supermatrices of refined labels is discussed in chapter three. Forth chapter introduces the notion of supermatrix of refined label vector spaces. Super matrix of refined labels of semivector spaces is introduced and studied and analysed in chapter five. Chapter six suggests the probable applications of these new structures. The final chapter suggests over hundred problems. We also thank Dr. K.Kandasamy for proof reading and being extremely supportive.
Zip Publishing, Ohio
supermatrices of refined labels, supermatrice
W.B. Vasantha Kandasamy & F. Smarandache. DSm super vector space of refined labels. Ohio: Zip Publishing, 2011
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