• Dr. G. Nanaji Rao
• S.Sujatha Kumari

The concept of *-epimorphism between Pseudo-complemented Almost Semilattices (PCASLs) L and M is introduced and proved that if f:L→M is a *-homomorphism, then ker(f) is a kernel ideal of L. It is proved that f:L→M is a *-epimorphism, then the mappings (f ) ⃗ : P(L) →P(M) and (f ) ⃖: P(M) →P(L) preserves kernel ideals. If L and M are *-commutative PCASLs in which 〖x≤x〗^(**), for all x and if f:L→M is *-epimorphism then established a lattice epimorphism (f ) ⃗_k , between complete implicative lattices KI(L) and KI(M) proved that (f ) ⃗_k is dually range closed. It is proved that complete lattices KI(L) and I(S(L)) of all ideals in the Boolean algebra S(L) of all *-elements in *-commutative PCASL L are isomorphic. The concept of co-kernel of a *-congruence on PCASL L is introduced and proved that if L is a *-commutative PCASL in which 〖x≤x〗^(**) for all x∈L and K is a filter of L, then the relation S_K on L defined by 〖(x,y)∈S〗_K if and only if x∘t=y∘t, for some t∈K is the smallest *-congruence with co-kernel K. Also, introduced the concept of *-filter in PCASL L and proved that if K is *-filter of *-commutative PCASL L then the *-congruence S_K∨ψ is the largest *-congruence with co-kernel K, where ψ is a relation on L defined by (x,y)∈ψ if and only if x^(**)=y^(**) which is a *-congruence.

"*-epimorphisms in Pseudo-complemented Almost Semilattices", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 2, page no.608-619, February-2019, Available :http://www.jetir.org/papers/JETIR1902B89.pdf

"*-epimorphisms in Pseudo-complemented Almost Semilattices", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 2, page no. pp608-619, February-2019, Available at : http://www.jetir.org/papers/JETIR1902B89.pdf