That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and...That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Hom (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory, all these results generalize the corresponding ones related to topological semigroups or topological groups.展开更多
In this paper twe prove that the inverse limit of metra-projective modules (meta-injective modules resp. ) is also meta-projective (meta-injective resp. ). Let K be a field f R1, R2 be K-algebras, we also obtain a suf...In this paper twe prove that the inverse limit of metra-projective modules (meta-injective modules resp. ) is also meta-projective (meta-injective resp. ). Let K be a field f R1, R2 be K-algebras, we also obtain a sufficient condition for lgldim (R1 R2,)≥lgldim R1+lgldimR2, and wgldim (R1 R2) ≥wgldimR1 +wgldimR2展开更多
文摘That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Hom (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory, all these results generalize the corresponding ones related to topological semigroups or topological groups.
文摘In this paper twe prove that the inverse limit of metra-projective modules (meta-injective modules resp. ) is also meta-projective (meta-injective resp. ). Let K be a field f R1, R2 be K-algebras, we also obtain a sufficient condition for lgldim (R1 R2,)≥lgldim R1+lgldimR2, and wgldim (R1 R2) ≥wgldimR1 +wgldimR2
