| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Research Abstract |
We study the structures of some algebraic systems as mathematical structure and examine algorithmic problems such as the word problem. In particular, we study the word problem of amalgamated free products of commutative inverse semigroups in the class of inverse semigroups. In addition, we clarify the algebraic structure of completely regular semigroups satisfying a certain equation. In particular, we completely characterize Rees matrix semigroup representations of completely simple semigroups. Then we obtain some results on varieties of completely regular semigroups satisfying the equation. We also obtain a theorem for orthocryptogroups similar to the Krull-Schimidt theorem in group theory. On the other hand, we examine designs like Latin squares on the surface of squares and applied to construct a Sudoku-type puzzle.
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