bordered ge-algebras

The notions of (transitive, commutative, antisymmet ric) bordered ge-algebras are introduced, and their properties are investigated. relations between a bordered ge-algebra and a bounded hilbert algebra are stated, and the conditions under which every bordered ge-algebra (resp., bounded hilbert algebra) can be a bounded hilbert algebra (resp., bordered ge-algebra) are found. the concept of duplex bordered ge-algebras is introduced, and its properties are investigated. relations between an antisym metric bordered ge-algebra and a duplex bordered ge-algebra are discussed, and the conditions under which an antisymmetric bor dered ge-algebra can be a duplex ge-algebra are established. a characterization of a duplex bordered ge-algebra is provided. a new bordered ge-algebra called cross bordered ge-algebra which is wider than duplex bordered ge-algebra is introduced, and its properties are investigated. relations between a duplex bordered ge-algebra and a cross bordered ge-algebra are considered.