On Regular Elements in an Incline | Zendy

A. Meenakshi | Zendy; S. Anbalagan | Zendy

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On Regular Elements in an Incline

Author(s) -

A. Meenakshi,

S. Anbalagan

Publication year - 2010

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2010/903063

Subject(s) - mathematics , idempotence , maximal element , involution (esoterism) , generalization , inverse , element (criminal law) , lattice (music) , pure mathematics , distributive property , set (abstract data type) , mathematical analysis , geometry , physics , politics , computer science , political science , acoustics , law , programming language

Inclines are additively idempotent semirings in which products are less than (or) equal to either factor. Necessary and sufficient conditions for an element in an incline to be regular are obtained. It is proved that every regular incline is a distributive lattice. The existence of the Moore-Penrose inverse of an element in an incline with involution is discussed. Characterizations of the set of all generalized inverses are presented as a generalization and development of regular elements in a ∗-regular ring

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