6533b7d2fe1ef96bd125e8ef

RESEARCH PRODUCT

Extending the star order to Rickart rings

Jānis Cīrulis

subject

CombinatoricsAlgebra and Number TheoryMathematics::Commutative Algebra010201 computation theory & mathematicsMathematics::Rings and AlgebrasOrder structureLattice properties010103 numerical & computational mathematics0102 computer and information sciences0101 mathematics01 natural sciencesMathematics

description

Star partial order was initially introduced for semigroups and rings with (proper) involution. In particular, this order has recently been studied on Rickart *-rings. It is known that the star order in such rings can be characterized by conditions not involving involution explicitly. Owing to these characterizations, the order can be extended to certain special Rickart rings named strong in the paper; this extension is the objective of the paper. The corresponding order structure of strong Rickart rings is studied more thoroughly. In particular, the most significant lattice properties of star-ordered Rickart *-rings are successfully transferred to strong Rickart rings; also several new results are obtained.

yearjournalcountryeditionlanguage
2015-10-22Linear and Multilinear Algebra
https://doi.org/10.1080/03081087.2015.1095858