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N. S. Gopalakrishnan ¹, N. Ramabhadran ¹, R. Sridharan ¹

Affiliations
1 Tata Institute of Fundamental Research, Bombay, IN

Abstract

In the three first propositions of this note we give sufficient conditions under which the relative left global dimension of a pair (Λ, T), where Λ is a ring and T a subring, is 0 or ∞.

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Leela Devi ¹, N. Ramabhadran ²

Affiliations
1 Department of Mathematics, Seethalakshmi Ramaswami College, Tiruchirapalli, Tamil Nadu, IN
2 Department of Mathematics, Bharathidasan University, Tiruchirapalli, Tamil Nadu, IN

Abstract

A Characterisation of the pair of extensions over sheaves G₁ and G₂ of R-Lie Algebras, with abelian kernel A, which arise from an extension of the product sheaf G₁ © G₂ with the same abelian kernel A, is brought out. It is shown that the set C (G₁ G₂; A) of all equivalence classes of Cohesively related pairs of extensions forms an abelian group, which is a homomorphic image of H² (G₁, G₂;A).

Keywords

Locally Trivial Extension, Cohesively Related Pairs of Extensions, Almost Central Local Splitting Extensions.

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