@Article{M-10514, AUTHOR = {Khanna, Dr. Reema}, TITLE = {Introduction to the Almost Suslin Matrices-The Key Lemma}, JOURNAL = {Scientific Research Journal of Science, Engineering and Technology}, VOLUME = {4}, YEAR = {2026}, NUMBER = {1}, ARTICLE-NUMBER = {M-10514}, URL = {https://isrdo.org/journal/SRJSET/currentissue/introduction-to-the-almost-suslin-matrices-the-key-lemma}, ISSN = {2584-0584}, ABSTRACT = {The Suslin matrices exhibit interesting properties which lead to the Local Global Principle and other important results. In this paper, we follow the Suslin construction by defining a variant of the Suslin matrices which are named the Almost Suslin Matrices S_r^(λ,μ) (v,w), w.r.t. a pair of parameters λ,μ∈R. The Almost Suslin matrices, despite the parameters, satisfy properties which can be used to derive stronger results. We define a special product ⟨⟨v,w⟩⟩ for v,w∈M_1(r+1)  (R). This helps us to derive results which finally leads us to our goal of proving the Key Lemma.}, DOI = {} }