Abstract: Linear resolution is an essential technique in commutative algebra to study invariants such as Betti numbers, projective dimension, and regularity. These invariants play a considerable role in learning the topologies of different algebraic structures. Here, we study a construction known as linearization. Linearization is a way of constructing an ideal from a monomial ideal J in a single degree but in a polynomial ring with more variables. The new ideal Lin(J) has linear resolution and linear quotients. Furthermore, we discuss another technique, equification, to generalize the linearization to all the monomial ideals. Equification converts a non-equigenerated monomial ideal J to an equigenerated monomial ideal J equif in a polynomial ring with one more variable. We see the connection between the syzygies of J and J equif and investigate their Betti numbers. Moreover, we look through the Betti splitting of Lin(J). We observe that how the Betti splitting of Lin(J) depends on the order of the generators of Lin(J).

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