Some Studies Of E-Invertible Matrices Over Commutative Antirings

The invertible matrix over a semiring has always been concerned by the scholars,so that many scholors have studied the equivalent characterizations of the invertible matrix over some special semirings and the properties of the invertible matrix.In 2018,Zhang Lixia and Shao Yong generalize the invertible matrix over a commutative semiring,the definition of the e-invertible matrix is introduced,where e is a nonzero multiplicative idempotent element over commutative semirings.This thesis will study the e-invertible matrix over a commutative antiring and its application over a commutative information algebra The main results are as follows.First,e-invertible matrix over a commutative antiring is discussed.The equivalent characterizations of invertible matrices over commutative antirings are given from different aspects.The relationship between semilinear transformation on a semilinear space and e-invertible matrices over commutative antirings are revealed..Second,study on e-invertible matrix over a commutative information algebra and the structure of semigroup that e-invertible matrices with respect to matrix multiplication is studied.The equivalent characterizations of e-invertible matrices over commutative information algebras and the basic form of the e-invertible matrices are given.Reveal the relationship between e-invertible matrix semigroup and nth symmetric groups.Furthmore,the decomposition theorem of maximal subgroup of e-invertible matrix semigroup is given.Third,semilinear space over a commutative information algebra is investigated.By studying the characterizations of e-invertible matrix over commutative information algebras,the relationship between the base of semilinear space eV_n(S)and the column vector of e-invertible matrix over commutative information algebras are discussed.