Relations among Matrices over a Semiring

被引：3

作者：

Killingbeck, Dylan ^{[1
]}

Teixeira, Milene Santos ^{[2
]}

Winter, Michael ^{[1
]}

机构：

[1] Brock Univ, Dept Comp Sci, St Catharines, ON L2S 3A1, Canada

[2] Univ Fed Santa Maria, Dept Comp Sci, BR-97119900 Santa Maria, RS, Brazil

来源：

RELATIONAL AND ALGEBRAIC METHODS IN COMPUTER SCIENCE (RAMICS 2015) | 2015年 / 9348卷

关键词：

LINEAR ALGEBRA;

D O I：

10.1007/978-3-319-24704-5_7

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

If I-x (S) denotes the set of (multiplicative) idempotent elements of a commutative semiring S, then a matrix over S is idempotent with respect to the Hadamard product iff all its coefficients are in Ix (S). Since the collection of idempotent matrices can be seen as an embedded structure of binary relations inside the category of matrices over S, we are interested in the relationship between the two structures. In particular, we are interested under which properties the idempotent matrices form a (distributive) allegory.

引用

页码：101 / 118

页数：18

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