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idempotent 2x2 matrices over linearly ordered abelian groups
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نویسنده
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kutti marilyn ,laan valdis
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منبع
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categories and general algebraic structures with applications - 2024 - دوره : 21 - شماره : 1 - صفحه:1 -17
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چکیده
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In this paper we study the multiplicative semigroup of 2 × 2 matrices over a linearly ordered abelian group with an externally added bot tom element. the multiplication of such a semigroup is defined by replacing addition and multiplication by join and addition in the usual formula defining matrix multiplication. we show that there are four types of idempotents in such a matrix semigroup and we determine which of them are 0-primitive. we also prove that the poset of idempotents of such a matrix semigroup with respect to the natural order is a lattice. it turns out that such a matrix semigroup is inverse or orthodox if and only if the abelian group is trivial.
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کلیدواژه
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matrix ,linearly ordered abelian group ,0-primitive idempotent ,full idempotent ,regular semigroup
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آدرس
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university of tartu, institute of mathematics and statistics, estonia, university of tartu, institute of mathematics and statistics, iran
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پست الکترونیکی
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valdis.laan@ut.ee
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Authors
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