Shahrood University of Technology Journal of Algebraic Systems 2345-5128 14 2 2026 04 01 t-PRIME SUBMODULES AND THEIR DECOMPOSITIONS 369 381 3742 10.22044/jas.2024.14373.1822 EN Javad Moghaderi Department of Mathematics, University of Hormozgan, Bandar Abbas, Hormozgan, Iran. Adnan Tercan Department of Mathematics, Hacettepe University Beytepe Campus, Beytepe/ANKARA, Turkey. Journal Article 2024 03 28 Let $R$ be a commutative ring with identity. For $t\in N$, a proper submodule $N$ of an $R$-module $M$ is called a t-prime submodule if $rm\in N~(r\in R, m\in M)$, then $m\in N$ or $r^t\in (N:_RM)$. We obtain some other characterizations of t-prime submodules. Also by some other notions like t-secondary submodules, various properties of t-prime submodules are investigated. To this end, we deal with irreducible as well as reduced t-prime decompositions of a submodule. We provide several examples with illustrate our results. https://jas.shahroodut.ac.ir/article_3742_83aeb62dca792b2e1b0978312d2a2581.pdf